CN110969356A - Method and system for setting index threshold based on normal distribution - Google Patents
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Abstract
The invention discloses a method and a system for setting an index threshold based on normal distribution, belongs to market state index analysis, and aims to solve the technical problem of how to obtain a state value reflecting the market state of a cigarette. The method comprises the steps of fitting a normal distribution probability density function through historical basic data based on normal distribution, taking the basic data as input, and obtaining a corresponding index threshold according to the normal distribution probability density function. The system comprises: the acquisition module is used for acquiring historical basic data to prepare the data for constructing normal distribution; the function building module is used for calculating the mean value and the standard deviation of historical basic data and obtaining a normal distribution probability density function corresponding to the basic data according to the normal distribution probability density function; and the threshold calculation module is used for calculating and outputting the index threshold corresponding to the basic data through the cumulative distribution function of normal distribution and the inverse function thereof.
Description
Technical Field
The invention relates to the field of market state index analysis, in particular to a method and a system for setting an index threshold value based on normal distribution.
Background
The threshold is a limit, so the threshold is also called a critical value, is a lowest value or a highest value which can generate an effect, is widely applied to various aspects including architecture, biology, flight, chemistry, telecommunication, electricity, psychology and the like, and in the process of researching the market state of cigarettes, the concept of the threshold is also introduced, but the setting of the threshold is often manually set according to historical experience.
In the research of cigarette market, the value of an index reflecting the market state, such as the order face, the order rate, the order satisfaction rate, the intersection investment ratio and the like, is often considered. Satisfactory state values are different for different cigarettes, and an empirical value is often used for the state table value; the status value that should be noticed by the marketer is also different, and is often an empirical value.
How to obtain the state value reflecting the cigarette market state is a technical problem to be solved.
Disclosure of Invention
The technical task of the invention is to provide a method and a system for setting an index threshold based on normal distribution to solve the problem of how to obtain a state value reflecting the cigarette market state.
In a first aspect, the invention provides a method for setting an index threshold based on normal distribution, which is based on normal distribution, fits a normal distribution probability density function through historical basic data, and obtains a corresponding index threshold according to the normal distribution probability density function by taking the basic data as input.
Preferably, the method comprises the steps of:
acquiring historical basic data to prepare data for constructing normal distribution;
calculating the mean value and the standard deviation of historical basic data, and obtaining a normal distribution probability density function corresponding to the basic data according to the normal distribution probability density function;
and calculating and outputting an index threshold corresponding to the basic data through a cumulative distribution function of normal distribution and an inverse function thereof.
Preferably, the method for calculating and outputting the index threshold corresponding to the basic data through the cumulative distribution function of the normal distribution and the inverse function thereof comprises the following steps:
normalizing the basic data through an accumulative distribution function to obtain corrected basic data;
and solving an index threshold corresponding to the corrected basic data through an inverse function of the accumulated distribution function.
Preferably, the corrected basic data is 0.1 × S;
where f (x) is a normal distribution probability density function.
Preferably, the normal distribution probability density function is:
where μ denotes the mean and σ denotes the standard deviation.
Preferably, the normal distribution setting index threshold is used for reflecting the cigarette market state;
the basic data is the order foot face.
In a second aspect, the present invention provides a system for setting an index threshold based on a normal distribution, wherein a market state value is calculated by the method for setting an index threshold based on a normal distribution according to any one of the first aspect, the system comprising:
the acquisition module is used for acquiring historical basic data to prepare data for constructing normal distribution;
the function building module is used for calculating the mean value and the standard deviation of historical basic data and obtaining a normal distribution probability density function corresponding to the basic data according to the normal distribution probability density function;
and the threshold calculation module is used for calculating and outputting the index threshold corresponding to the basic data through the cumulative distribution function of normal distribution and the inverse function thereof.
Preferably, the threshold calculation module has the following functions:
normalizing the basic data through an accumulative distribution function to obtain corrected basic data;
and solving an index threshold corresponding to the corrected basic data through an inverse function of the accumulated distribution function.
Preferably, the corrected basic data is 0.1 × S;
where f (x) is a normal distribution probability density function.
Preferably, the normal distribution probability density function is:
where μ denotes the mean and σ denotes the standard deviation.
The method and the system for setting the index threshold based on normal distribution have the following advantages that:
1. by the method, corresponding index thresholds can be obtained for different basic data, and the method is suitable for different basic data;
2. the specified index threshold value reflecting the cigarette market state is calculated by constructing normal distribution, so that the following problems can be avoided: for the mature specification, the distribution of the foot-ordering surface is concentrated, if the early warning value is directly calculated by using the quantile 10%, the market optimization is difficult even if the early warning value is judged to be early warning, the early warning value is calculated by constructing normal distribution, the foot-ordering surface is concentrated and distributed on two sides of a symmetry axis x which is equal to mu, the input area ratio is 0.1, and the condition cannot occur.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
The invention is further described below with reference to the accompanying drawings.
Fig. 1 is a flow chart of a method for setting an index threshold based on normal distribution in embodiment 1.
Detailed Description
The present invention is further described in the following with reference to the drawings and the specific embodiments so that those skilled in the art can better understand the present invention and can implement the present invention, but the embodiments are not to be construed as limiting the present invention, and the embodiments and the technical features of the embodiments can be combined with each other without conflict.
The embodiment of the invention provides a method and a system for setting an index threshold based on normal distribution, which are used for solving the technical problem of how to obtain a state value reflecting the cigarette market state.
Example 1:
the invention discloses a method for setting an index threshold based on normal distribution, which is characterized in that based on normal distribution, a normal distribution probability density function is fitted through historical basic data, the basic data is used as input, and a corresponding index threshold is obtained according to the normal distribution probability density function.
The method comprises the following steps:
s100, acquiring historical basic data to prepare data for constructing normal distribution;
s200, calculating the mean value and the standard deviation of historical basic data, and obtaining a normal distribution probability density function corresponding to the basic data according to the normal distribution probability density function;
and S300, calculating an index threshold corresponding to the output basic data through the cumulative distribution function of normal distribution and the inverse function of the cumulative distribution function.
In step S300, an index threshold corresponding to output basic data is calculated by the cumulative distribution function of normal distribution and its inverse function, including the following steps:
s310, normalizing the basic data through an accumulative distribution function to obtain corrected basic data;
and S320, solving an index threshold corresponding to the corrected basic data through the inverse function of the cumulative distribution function.
Wherein the corrected basic data is 0.1 xS;
where f (x) is a normal distribution probability density function.
The normal distribution probability density function is:
where μ denotes the mean and σ denotes the standard deviation.
In this embodiment, the normal distribution setting index threshold is used for reflecting the cigarette market state, and the collected basic data is the order. The method comprises the following specific steps:
firstly, data preparation for constructing normal distribution is carried out: selecting the weekly order of all cities in the country of 18 years of the Heiyixi as basic data;
then, a normal distribution is constructed: solving the mean value and the standard deviation of the foot-fixing surface, and obtaining a normal distribution probability density function of the cigarette foot-fixing surface according to the probability density function of normal distribution;
and finally, solving a threshold value according to a normal distribution probability density function of the cigarette binding foot surface: for example, 0.1 of the area ratio which should be noticed is input (the area enclosed by the normal distribution curve and the x-axis is 1), and the threshold corresponding to the area ratio is calculated and output by the cumulative distribution function of the normal distribution and the inverse function thereof.
The specific process of solving the threshold value according to the normal distribution probability density function of the cigarette binding foot surfaceComprises the following steps: the underlying data is first normalized by the cumulative distribution function, since the order surface cannot be smaller than 0 and larger than 1, (- ∞,0) and (1, + ∞) clearly do not match the business logic, and the total area is after this portion is removed
Apparently less than 1, the area ratio which should be noted after normalization processing is 0.1 × S; and then, calculating a threshold corresponding to the corrected area through an inverse function of the cumulative distribution function.
The following problems can be effectively avoided by constructing normal distribution to calculate the early warning value: for the mature specification, the distribution of the foot-ordering surface is concentrated, if the early warning value is directly calculated by using the quantile 10%, the market optimization is difficult even if the early warning value is judged to be early warning, the early warning value is calculated by constructing normal distribution, the foot-ordering surface is concentrated and distributed on two sides of a symmetry axis x which is equal to mu, the input area ratio is 0.1, and the condition cannot occur.
Example 2:
the invention discloses a system for setting an index threshold based on normal distribution, which comprises an acquisition module, a function construction module and a threshold calculation module. The acquisition module is used for acquiring historical basic data to prepare the data for constructing normal distribution; the function building module is used for calculating the mean value and the standard deviation of historical basic data and obtaining a normal distribution probability density function corresponding to the basic data according to the normal distribution probability density function; and the threshold calculation module is used for calculating and outputting the index threshold corresponding to the basic data through the cumulative distribution function of normal distribution and the inverse function thereof.
The threshold value calculation module has the following functions: normalizing the basic data through an accumulative distribution function to obtain corrected basic data; and solving an index threshold corresponding to the corrected basic data through an inverse function of the accumulated distribution function.
The corrected basic data is 0.1 multiplied by S;
where f (x) is a normal distribution probability density function.
The normal distribution probability density function is:
where μ denotes the mean and σ denotes the standard deviation.
The system for setting the index threshold based on the normal distribution can execute the method for setting the index threshold based on the normal distribution disclosed by the embodiment of the invention, and can calculate the index threshold of the cigarette market state by executing the method.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (10)
1. A method for setting an index threshold value based on normal distribution is characterized in that a normal distribution probability density function is fitted through historical basic data based on normal distribution, the basic data is used as input, and a corresponding index threshold value is obtained according to the normal distribution probability density function.
2. The method according to claim 1, wherein the method comprises the following steps:
acquiring historical basic data to prepare data for constructing normal distribution;
calculating the mean value and the standard deviation of historical basic data, and obtaining a normal distribution probability density function corresponding to the basic data according to the normal distribution probability density function;
and calculating and outputting an index threshold corresponding to the basic data through a cumulative distribution function of normal distribution and an inverse function thereof.
3. The method according to claim 2, wherein the index threshold corresponding to the basic data is calculated and output by an accumulative distribution function of normal distribution and an inverse function thereof, and the method comprises the following steps:
normalizing the basic data through an accumulative distribution function to obtain corrected basic data;
and solving an index threshold corresponding to the corrected basic data through an inverse function of the accumulated distribution function.
4. The method according to claim 3, wherein the modified basic data is 0.1 × S;
where f (x) is a normal distribution probability density function.
5. The method according to claim 2, 3 or 4, wherein the normal distribution probability density function is:
where μ denotes the mean and σ denotes the standard deviation.
6. The method for setting the index threshold based on the normal distribution according to claim 1, 2, 3 or 4, wherein the normal distribution setting index threshold is used for reflecting the cigarette market state;
the basic data is the order foot face.
7. A system for setting an index threshold value based on a normal distribution, wherein a market state value is calculated by the method for setting an index threshold value based on a normal distribution according to any one of claims 1 to 6, the system comprising:
the acquisition module is used for acquiring historical basic data to prepare data for constructing normal distribution;
the function building module is used for calculating the mean value and the standard deviation of historical basic data and obtaining a normal distribution probability density function corresponding to the basic data according to the normal distribution probability density function;
and the threshold calculation module is used for calculating and outputting the index threshold corresponding to the basic data through the cumulative distribution function of normal distribution and the inverse function thereof.
8. The system according to claim 7, wherein the threshold calculation module has the following functions:
normalizing the basic data through an accumulative distribution function to obtain corrected basic data;
and solving an index threshold corresponding to the corrected basic data through an inverse function of the accumulated distribution function.
9. The system according to claim 8, wherein the modified basic data is 0.1 xs;
where f (x) is a normal distribution probability density function.
10. The system according to claim 7, 8 or 9, wherein the normal distribution probability density function is:
where μ denotes the mean and σ denotes the standard deviation.
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| CN112783884A (en) * | 2021-01-29 | 2021-05-11 | 浪潮软件股份有限公司 | Data optimization method based on normal distribution |
| CN114609372A (en) * | 2022-02-18 | 2022-06-10 | 江苏徐工工程机械研究院有限公司 | Engineering machinery oil monitoring system and method based on maximum entropy |
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