JP6192432B2 - Risk weighing system - Google Patents

Description

  The present invention relates to a risk quantification technique, and in particular, a risk metric that estimates a probability distribution and its parameters with respect to an accident occurrence frequency and a loss amount, and measures the risk using a probability distribution function of the estimated number of accidents and loss distribution. The present invention relates to a system that performs display for evaluating the degree of fit between an estimated distribution and accident data.

  In general, business operations can encounter various risks such as system failures, clerical errors, and fraud. For this reason, it is required to collect accident data, measure the risk, and take measures against the risk. In general risk quantification, for example, as in Patent Document 1 and Non-Patent Document 1, a risk amount called VaR is calculated.

  Specifically, first, the accident number distribution is estimated from the number of accidents per certain period of the collected accident data, and the loss distribution per accident is estimated from the loss amount of the accident that occurred. Then, by Monte Carlo simulation, what is the processing to calculate the total loss per fixed period by summing up the loss amount generated from the above loss amount distribution using the above accident number distribution? Generate a distribution of the total loss by repeating the number of times. Then, from the generated distribution of the total loss, the total loss at a predetermined quantile is defined as VaR (Value at Risk). For example, a distribution of the total loss that can occur in one year is generated by simulation, and a huge loss that can occur once in a hundred years or once in a thousand years is measured therefrom.

  Here, as a method of evaluating the degree of fit between the estimated probability distribution and the accident data, in addition to quantitative test methods such as Kolmogorov-Smirnov test and Anderson-Darling test as in Non-Patent Document 1, pp plot and qq plot For example, there is a technique for determining the degree of fit using a graph.

  In addition, as a risk measurement method, a method is used in which a highly accurate risk measurement can be performed by estimating a distribution for each of a plurality of risk scenarios and totaling the total loss in a simulation.

Japanese Patent No. 4241083

Operational risk management system of financial institutions (Financial Inspection Manual Handbook Series) p64-65, p114-119

  In general, logarithmic normal distribution and generalized Pareto distribution are often used to estimate the loss distribution, but it is known that it does not fit well with accident data. The current theoretical distribution function has not yet been discovered.

  For this reason, quantitative evaluation by testing often does not give very good results. The test evaluates whether or not the data follows a specific probability distribution, and is not intended to be used for comparison of the degree of fit to a plurality of estimated distribution candidates. Therefore, it is necessary for humans to empirically evaluate the fit of the estimated distribution while looking at graphs such as the q-q plot, and to examine VaR for the estimated distribution candidate that seems to be appropriate. At this time, as a display method for evaluating the fit of the estimated distribution, a p-p plot and a q-q plot are used in addition to the cumulative distribution function plot.

  The display method of the cumulative distribution function is a method of displaying a cumulative distribution function of an estimated distribution and a graph using a ratio between the loss amount of accident data and the total number of accidents less than that. The pp plot and qq plot are graphs of the accident data graph and the estimated distribution graph with the horizontal axis in the pp plot and the vertical axis variable in the qq plot as parameters. It is displayed on a two-dimensional graph with a set of values as coordinates.

Accident data generally tends to decrease in frequency more rapidly as the amount of loss increases, so it is difficult to evaluate the overall fit from high frequency low loss to low frequency high loss by graph display. is there.
In addition, the logarithm value of the loss amount is widely used. In this case, the ratio of the difference in loss amount is displayed as a difference on the graph. The difference between the loss of 1 million yen and the loss of 2 million yen is expressed as the same difference, and there is a problem that it is difficult to evaluate the difference in fit on a loss basis.
Further, since the cumulative distribution of the estimated distribution often has a probability of 1 when the amount of loss is infinite, there is a problem that it is difficult to consider the maximum amount of loss of accident data in the evaluation of the fit.

  In view of the above-described problems, an object of the present invention is to make it easy to evaluate the degree of fit in the graph display of accident data and estimated distribution in a risk weighing system.

In order to achieve the above object, the present invention provides the following configurations.
An aspect of the present invention provides a specified probability distribution function and a specified parameter estimation method for accident data for distribution estimation selected according to a predetermined estimation condition from collected accident data including an accident occurrence date and time and a loss amount. A distribution estimation means that estimates the accident number distribution and loss distribution by applying
Simulation means for generating a random number according to the estimated accident number distribution and the loss amount distribution to calculate a total loss occurring within a predetermined period, a simulation means for executing a plurality of times;
In a risk weighing system comprising: a risk weighing unit that calculates a total loss of a specified quantile in the total loss data obtained by the simulation unit, the processing device includes:
For each estimated distribution candidate estimated by a plurality of probability distribution functions and a plurality of parameter estimation methods representing the accident number distribution and loss distribution in the distribution estimation means,
In order to evaluate the degree of fit between the estimated distribution and the distribution estimation accident data, the integral function of the cumulative distribution inverse function of the estimated distribution, the loss amount based on the distribution estimation accident data, and a certain loss amount or less It has an estimated distribution evaluation means for displaying on a graph the data represented by the ratio of the cumulative number of accidents to the total number of accidents and the cumulative loss amount below a certain loss amount.

In the estimated distribution evaluation means in the above aspect,
For the accident data for distribution estimation, the horizontal axis is the ratio of the total number of accidents with a certain loss amount or less to the total number of accidents, and the vertical axis is the cumulative loss amount or its logarithm, or the ratio of the cumulative loss amount to the total loss Display the graph,
For the integral function of the cumulative distribution inverse function of the estimated distribution, a graph in which the horizontal axis is the probability and the vertical axis is the value of the integral function or its logarithmic value, or the ratio to the value of the integral function when the probability is 1. Display
It is preferable to display these graphs side by side or superimposed.

In the estimated distribution evaluation means in the above aspect,
It is preferable to display the horizontal axis of the graph with respect to the accident data and the horizontal axis of the graph with respect to the integral function of the cumulative distribution inverse function of the estimated distribution as an accident loss amount per case.

In the estimated distribution evaluation means in the above aspect,
A graph in which the horizontal axis variable is the parameter when the accident data and estimated distribution graphs are superimposed, and the vertical and horizontal axes are pairs of values on the accident data and estimated distribution graphs. Is preferably displayed.

  In the present invention, the integral function for the cumulative distribution inverse function of the estimated distribution and the cumulative loss from the minimum loss amount in the accident data are used, and a graph that can compare these is displayed. Specifically, taking the probability on the horizontal axis, the cumulative loss amount from the lowest loss that occurs at that probability is calculated for the accident data and the estimated distribution, and the graph is displayed with the value as the vertical axis. In addition, the horizontal axis represents the amount of loss, and the vertical axis represents the cumulative amount of loss for accidents below that amount. These specified distributions and accident data graphs can be displayed superimposed. In addition, the horizontal axis of these graphs is used as a parameter, and the cumulative loss amounts of each of the estimated distribution and accident data are used as coordinates, and the vertical and horizontal axes are displayed to show the fit. Make it possible to evaluate on a loss basis.

  By displaying the graphs using these plotting methods, quantitative evaluations using existing pp plots, qq plots, and tests, and VaR values from simulations are displayed in any combination for each estimated distribution candidate. It is possible to provide support for selecting VaR that seems appropriate from the candidates.

  According to the present invention, it is possible to display the fit between the accident data and the estimated distribution corresponding thereto in the risk weighing system in a well-balanced manner from the high frequency low loss to the low frequency high loss, and the average value of the estimated distribution is finite. In this case, the maximum loss point in the accident data can be plotted, and the fit of the estimated distribution can be evaluated on a loss basis.

FIG. 1 is a system configuration diagram of an example of the present embodiment. FIG. 2 is a diagram illustrating an example of the data structure of the present embodiment. FIG. 3 is a flowchart showing an example of the overall processing of this embodiment. FIG. 4 is a flowchart showing an example of the estimation accident data table generation process of FIG. FIG. 5 is a flowchart showing an example of the distribution estimation process of FIG. FIG. 6 is a flowchart showing an example of the risk measurement process of FIG. FIG. 7 is a diagram illustrating a graph display example in the output processing of FIG.

  Hereinafter, embodiments of the risk measurement system of the present invention will be described with reference to the drawings shown as an example. In this embodiment of the risk measurement system, accident data is collected by adding risk management means to this system or by a separate risk management system. This system refers to accident data from there and based on it. Distribution estimation and risk measurement. Therefore, accident data collection aspects are not included in this system.

  In general risk measurement, the distribution is estimated for each risk scenario to which the accident belongs, but in risk measurement, it is only necessary to add the random number of losses for each scenario to make the total loss. In the example of the embodiment, processing such as estimation for each risk scenario and total risk metric is omitted, and description will be made assuming that there is one scenario.

  FIG. 1 is a system configuration diagram illustrating an example of an embodiment of the present system. The system includes an input device 101, an output device 102 such as a printer, a display device 103 such as a display, a processing device 104, and a database (DB) 110.

  The processing device 104 includes a series of function processing units 105 including an estimation accident data generation unit 106, a distribution estimation unit 107, a risk measurement unit 108, and an output processing unit 109. These function processing units 105 are realized by reading a predetermined program installed in the processing device 104, which is a computer, into a memory and executing the program by the CPU.

  The DB 110 includes an accident data table 111 storing collected accident data, a distribution estimation accident data table 112 used for distribution estimation, an estimated distribution table 113 storing estimated distributions and parameters thereof, and distribution estimation accident data. Accident data statistic table 114 that stores various statistics for the estimated distribution, an estimated distribution statistic table 115 that stores various statistics for the estimated distribution, and a simulation result table 116 that stores the total loss calculated in the simulation. The accident data table 111 may be held by another system that performs the accident data collection process. In this case, it is only necessary that the data can be referred to from this system.

2A to 2F are diagrams illustrating an example of the data structure of the present embodiment.
The accident data table 111 in FIG. 2A stores information on the accident that occurred, “item number” 201 as the ID for identifying the accident data, “occurrence date and time” 202 of the accident, “ Loss amount "203," accident code "204, and the like. The accident code includes, for example, information necessary for estimation for each risk scenario, such as information for identifying the business type of the accident that has occurred and its cause, and the ID of the employee in charge.

  In the accident estimation data table 112 for distribution estimation in FIG. 2 (b), accident data used for estimating the number of accidents distribution and the loss amount distribution is selected and acquired from the accident data table 111, and the accident data for distribution estimation is acquired. Store as. “Data set ID” 205 for identifying the estimation unit, “estimation condition” 206 for storing conditions such as the period and risk scenario of the accident data used for estimation, and “item number 201 for storing the estimation condition 206” Accident data item number "207," accident number ratio "208," cumulative loss amount "209, and" accumulated loss amount ratio "210 are stored.

  The accident data for distribution estimation is sorted in ascending order of the loss amount 203 with respect to the same data set ID. The accident number ratio 208, the cumulative loss amount 209, and the cumulative loss ratio 210 are calculated by sequentially accumulating the number of accidents or the loss amount from the minimum loss data. The accident number ratio 208 is a ratio of the cumulative number of accidents to the total number of accidents of the same data set ID. The cumulative loss amount ratio 210 is a ratio of the cumulative loss amount 209 to the total loss amount of the same data set ID. Further, these may be calculated as accumulation from the maximum loss amount as necessary, but are omitted in this embodiment.

  The estimated distribution table 113 in FIG. 2C stores a result of estimating a theoretical distribution that applies to the distribution estimation accident data table 112. It consists of “item number” 211 as an ID for specifying the distribution, “data set ID” 212 used for estimation, “distribution type ID” 213, “estimation method ID” 214, and “estimation parameter” 215. The distribution type ID 213 identifies a theoretical distribution such as a Poisson distribution or a lognormal distribution. The estimation method ID 214 identifies a parameter estimation method such as a least square method or a maximum likelihood method with respect to the distribution type ID 213. The parameters estimated by these are stored in the estimation parameter 215.

  Here, when the distribution type represents a mixed distribution of a plurality of distributions, the estimation parameter 215 stores each distribution function and its mixing rate. The distribution type ID 213 can identify which of the accident number distribution and the loss amount distribution is estimated.

  The accident data statistic table 114 in FIG. 2D includes a “data set ID” 216, a “statistic ID” 217, and a “statistic” 218. The estimated distribution statistic table 115 in FIG. 2E includes an “estimated distribution item number” 219, a “statistic ID” 220, and a “statistic” 221. These have the same structure except for the difference between the data set ID 216 that specifies the former accident data and the estimated distribution item number 219 that specifies the estimated distribution of the latter. Statistics IDs 217 and 220 are IDs for identifying types of statistics such as average, standard deviation, and median, and are used for distribution estimation, and test statistics for determining whether to reject as a candidate for estimated distribution, It is assumed that what is used for comparison of estimated distribution candidates is determined in advance. The statistics 218 and 221 are obtained by calculating the statistics specified by the statistics IDs 217 and 220 with respect to the accident data indicated by the data set ID 216 or the estimated distribution indicated by the estimated distribution item number 219, respectively. Store.

  The simulation result table 116 in FIG. 2F includes a “result item number” 222 for identifying one simulation result, a “data set ID” 223 of accident data used for the simulation, the number of trials in the simulation, and a random number. “Simulation condition” 224 representing seeds, “accident number distribution item number” 225, “loss amount distribution item number” 226 used in the simulation, and the ratio from the top to the total loss amount of trials obtained in the simulation “Probability” 227 representing the probability, and “VaR” 228 representing the total loss of the quantile indicated by the probability 227.

  In the accident number distribution item number 225 and the loss amount distribution item number 226, the estimated distribution item number 211 of the estimated distribution table 113 is stored. When a simulation is executed with a plurality of risk scenarios, these item numbers may be expanded to a list of scenario numbers.

  Generally, 90%, 99%, 99.9%, etc. are often used for the probability 227, but it is assumed that one or more of these values are set in advance. Instead of the probability 227, a simulation trial number may be stored, and the total loss total for the number of trials may be stored. In this case, VaR of the quantile specified as needed may be calculated each time. For example, it is possible to calculate a statistic that is not so important as a risk measurement result, such as an average of the total loss or a median.

FIG. 3 is a flowchart showing an example of the overall processing of this embodiment.
First, a distribution estimation accident data table 112 is generated from the accident data table 111 (step 301). Details will be described with reference to FIG.
Next, parameters of each probability distribution candidate are estimated with respect to the distribution estimation accident data table 112 generated in step 301, and an estimated distribution table 113 is created (step 302). Details will be described with reference to FIG.
Next, risk metric processing is executed using the estimated distribution table 113 estimated in step 302 (step 303). Details will be described with reference to FIG.
Next, an output process is executed (step 304), and the process ends.

  In the output process of step 304, a graph for evaluating the degree of fit between the distribution estimation accident data table 112 generated in step 301 and each estimated distribution estimated in step 302, and in steps 408 and 503 described later, The calculated statistics, VaR based on the simulation result obtained in step 303, etc. are displayed as a list or printed as necessary. An example of a graph display method will be described with reference to FIG.

  A series of these processes is performed on the data set of accident data for distribution estimation newly generated in Step 301. In addition, when using data generated, estimated, or measured in the past, it is possible to omit the corresponding step and input the data set ID, result item number, and the like to perform output processing. Note that it is easy to change the processing order so that the risk metric processing is performed only on the adopted distribution after evaluating the distribution fit to the estimated distribution candidate by the output processing.

FIG. 4 is a flowchart showing an example of the distribution estimation accident data table generation process in step 301 of FIG.
First, an estimation condition is input (step 401). At this time, if an estimation condition is set in advance, the condition can be used. For example, if it is determined from the currently accumulated accident data that data for the past five years will be used for risk measurement, the input of conditions can be omitted.

  Next, a list of accident data item numbers 201 satisfying the estimation condition is acquired from the accident data table 111 (step 402). Next, the list is sorted in ascending order of the loss amount (step 403). Next, the accident data item number list is stored in the accident data table 112 for distribution estimation (404). At this time, the newly generated ID is stored in the data set ID 205, and the estimation condition in step 401 is stored in the estimation condition 206.

Next, the accident number ratio of each accident data is calculated and stored in the accident number ratio 208 (step 405).
Next, the cumulative loss amount of each accident data is calculated and stored in the cumulative loss amount 209 (step 406).
Next, the ratio between the cumulative loss 209 and the total loss of accident data is calculated and stored in the cumulative loss ratio 210 (step 407).

Next, various preset statistics are calculated for the accident estimation data table 112 for distribution estimation, stored in the accident data statistics table 114 (step 408), and the process ends.
The statistic calculated in step 408 may store a value for each significant level of the test statistic. For example, in the Kolmogorov-Smirnov test, the standard changes depending on the number of data, and therefore, the value of the test statistic at the significance level of 1% or 5% can be stored in this table.

FIG. 5 is a flowchart showing an example of the distribution estimation process in step 302 of FIG.
First, the accident number distribution is estimated (step 501). Here, based on the number of accidents per unit period in the accident data table 112 for distribution estimation, the parameters of the distribution are estimated according to each specified theoretical distribution and estimation method. The estimation result is stored in the estimated distribution table 113.

  Next, the loss amount distribution is estimated (step 502). Here, based on the loss amount in the distribution estimation accident data table 112, the parameters of the distribution are estimated according to each specified theoretical distribution and estimation method. The estimation result is stored in the estimated distribution table 113.

  Next, various statistics are calculated for each distribution estimated in steps 501 and 502, stored in the estimated distribution statistics table 115 (503), and the process is terminated. This corresponds to the accident data statistic table 114 and is output by the output process 304, and is used to evaluate the degree of fit between the estimated distribution and the accident data.

FIG. 6 is a flowchart showing an example of the risk measurement process in step 303 of FIG.
Here, a Monte Carlo simulation based on each estimated distribution estimated in the distribution estimation process 302 is executed, and the risk amount is measured.

  First, simulation conditions are input (step 601). Simulation conditions include the number of trials and random number seed. In addition, if processing that excludes a combination of a specific accident number distribution and loss distribution to be simulated from candidates based on an evaluation of distribution fit by the output process 304 is excluded in advance A distribution combination list is also input as a simulation condition, and only a specified combination of estimated distributions can be simulated.

  Next, a list P is generated for information obtained by combining the estimated accident number distribution, the estimated distribution item number of the loss amount distribution, and the simulation conditions (step 602). Here, all combinations of the estimated accident number distribution and loss distribution are generated for the data set ID to be simulated. However, this processing can be omitted if the combination including those combinations is input in step 601.

  Next, “1” is substituted into a variable s representing an element of the list P (step 603). Next, while s is less than or equal to the number of elements in the list P (step 604), the following processing is looped.

  First, initialization is performed according to the simulation condition P [s] (step 605). Here, along with initialization of the number of simulation trials, random number seeds, etc., an array L for storing the total loss amount for the number of trials is prepared, and each element is initialized with zero.

  Next, “1” is substituted into a variable i representing the current number of trials (step 606). Next, while i is equal to or smaller than the number of trials specified by P [s] (step 607), the following processing is looped.

First, one random number according to the accident number distribution of P [s] is generated (step 608).
Next, random numbers according to the loss distribution of P [s] are generated by the number of accidents and added to L [i] (step 609). Next, 1 is added to i (step 610), and the process returns to step 607.
If the condition is No in step 607, first, the array L is sorted in ascending order (step 611), and VaR is calculated (step 612). Calculate VaR of quantile specified in advance. Interpolation may be performed, or the array L may be stored as it is.

Next, the simulation result of the condition P [s] is stored in the simulation result table 116 (step 613). Next, 1 is added to s (step 614), and the process returns to step 604.
If the condition in step 604 is No, the process ends.

FIG. 7 is a diagram illustrating an example of a display method of a graph displayed in the output process of the present embodiment.
As a graph to evaluate the fit between the estimated distribution and the accident data, the accident data is plotted with the amount of loss sorted in ascending order and the number of accidents, and the cumulative distribution function graph of the estimated distribution corresponds to it. It is a commonly used method to display the image. The graph based on the estimated distribution and the graph based on the accident data can be displayed side by side or superimposed.

  Since the vertical and horizontal axes are interchanged in FIG. 7A, the accident data is plotted with the accident number ratio and the loss amount in ascending order of the loss amount, and the estimated distribution is an inverse cumulative distribution function.

  Also, the plot of the q-q plot of FIG. 7B is a plot using two sets of the accident data and the estimated distribution using the variable on the horizontal axis of the graph of FIG. 7A as a parameter. . Using the qq plot, it can be seen that the closer the plotted point is to the dotted line of 45 degrees, the better the fit. However, the q-q plot cannot be plotted because the estimated distribution becomes infinite with respect to the maximum loss amount of accident data. For this reason, the broken line portion to the maximum loss is a dotted line.

  In the present embodiment, the above plotting method is extended to plot the ratio of the number of accidents against the amount of loss sorted in ascending order with respect to the accident data, and the cumulative loss amount, and integrate the inverse distribution function of the cumulative distribution of the estimated distribution there. Display function graphs correspondingly. That is, the graph of FIG. 7C is obtained by plotting the area from the probability “0” to the corresponding probability with respect to the value of the variable p in the graph of FIG. If the cumulative distribution function is F (x), the integral function L (p) of the inverse cumulative distribution function is the integral from the probability “0” to “p”,

It becomes. If the integration of the inverse cumulative distribution function cannot be transformed into four basic arithmetic operations, an approximate value may be calculated using an existing numerical integration method.

  Furthermore, with respect to the graph of FIG. 7 (c), the variable of the horizontal axis of the accident data and the estimated distribution is a parameter, and the set of the value of the accident data and the estimated distribution is the vertical axis as in the above q-q plot. What is plotted on the horizontal axis is the graph of FIG.

  Also, the integral function of the cumulative distribution inverse function of the estimated distribution is used as a function of the loss amount x.

It is good. Further, the vertical axis can be a logarithmic value of the integral function or a ratio with the value of the integral function when the probability is 1.

From the accident data, a graph of loss (horizontal axis) and cumulative loss (vertical axis) is plotted. Furthermore, it is possible to plot the cumulative loss amount on the vertical axis as a logarithmic value. Further, it is possible to plot the vertical axis as a ratio of the accumulated loss amount to the total loss amount.
The horizontal axis of the graph for the accident data and the horizontal axis of the graph for the integral function of the cumulative distribution inverse function of the estimated distribution may be displayed as the amount of accident loss per case.
Furthermore, it is possible to plot a graph in which the horizontal axis of the accident data and the estimated distribution is a parameter, and the set of the values of the accident data and the estimated distribution is the vertical axis and the horizontal axis.

  In addition, in these plotting methods, it is also possible to select one candidate estimated distribution and display a plurality of other estimated distributions in a superimposed manner.

101: input device 102: output device 103: display device 104: processing device 105: program 106: estimation accident data generation unit 107: distribution estimation unit 108: risk weighing unit 109: output processing unit 110: DB
111: Accident data table 112: Accident data table for distribution estimation 113: Estimated distribution table 114: Accident data statistic table 115: Estimated distribution statistic table 116: Simulation result table

Claims (4)

The number of accidents by applying the specified probability distribution function and the specified parameter estimation method to the accident data for distribution estimation selected from the collected accident data including the date and time of the accident and the amount of loss according to the specified estimation conditions Distribution estimation means for estimating distribution and loss distribution;
Simulation means for generating a random number according to the estimated accident number distribution and the loss amount distribution to calculate a total loss occurring within a predetermined period, a simulation means for executing a plurality of times;
In a risk weighing system comprising: a risk weighing unit that calculates a total loss of a specified quantile in the total loss data obtained by the simulation unit, the processing device includes:
For each estimated distribution candidate estimated by a plurality of probability distribution functions and a plurality of parameter estimation methods representing the accident number distribution and loss distribution in the distribution estimation means,
In order to evaluate the degree of fit between the estimated distribution and the distribution estimation accident data, the integral function of the cumulative distribution inverse function of the estimated distribution, the loss amount based on the distribution estimation accident data, and a certain loss amount or less A risk weighing system comprising: an estimated distribution evaluation unit that displays a ratio of the total number of accidents to the total number of accidents and data represented by a cumulative loss amount equal to or less than a certain loss amount on a graph. In the estimated distribution evaluation means,
For the accident data for distribution estimation, the horizontal axis is the ratio of the total number of accidents with a certain loss amount or less to the total number of accidents, and the vertical axis is the cumulative loss amount or its logarithm, or the ratio of the cumulative loss amount to the total loss Display the graph,
For the integral function of the cumulative distribution inverse function of the estimated distribution, a graph in which the horizontal axis is the probability and the vertical axis is the value of the integral function or its logarithmic value, or the ratio to the value of the integral function when the probability is 1. Display
The risk weighing system according to claim 1, wherein these graphs are displayed side by side or displayed in a superimposed manner. In the estimated distribution evaluation means,
The risk measurement system according to claim 2, wherein the horizontal axis of the graph for accident data and the horizontal axis of the graph for the integral function of the cumulative distribution inverse function of the estimated distribution are displayed as an accident loss amount per case. . In the estimated distribution evaluation means,
A graph in which the horizontal axis variable is the parameter when the accident data and estimated distribution graphs are superimposed, and the vertical and horizontal axes are pairs of values on the accident data and estimated distribution graphs. The risk weighing system according to claim 2, wherein the risk weighing system is displayed.

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