CN102324071A - Social cigarette stock estimation method based on stratified regression estimation - Google Patents

Abstract

The invention relates to a social cigarette stock estimation method based on stratified regression estimation. The method comprises the following steps of: (1) establishing a sample by using the stratified sampling method; (2) calculating the regression estimation value of each stratum; and (3) accumulating the regression estimation values of all strata to obtain the total social stock estimation value. By analyzing retail sample data and using the stratified regression estimation method, the social stock estimation value of each stratum is corrected with order quantity in the sample data as auxiliary variables, and the estimation data of each stratum is accumulated to obtain the corrected overall social cigarette stock estimation value. By using the estimation method provided by the invention, the social stock estimation value is more scientific and reliable. When other kinds of business data are investigated, the estimation value can be corrected through small sample size of sampling data by combining certain auxiliary variables, and the effect of getting two-folded results with half the effort is achieved.

Description

Cigarette social inventory method of estimation based on the hierarchical multiple regression estimation

Technical field

The present invention relates to tobacco business, relate in particular to cigarette social inventory method of estimation.

Background technology

Cigarette market, the whole nation has experienced after very fast in the past the growth, and the cigarette sale total amount is kept under the background of steady-state growth during 12, and the business model of " selling well " has progressively been changed in national commercial enterprise from " selling ".For cigarette enterprise sales department accurately holds the demand-supply relation,, supports the six smart targets of " how to sell, whom sells, how long how much sell, sell, who buys, who sells " for the collection of end message with analyze very necessaryly.

The cigarette social inventory refers to be in the cigarette stock at retail link (retail family), and it directly affects the supply of cigarette, is one of important indicator of reflection relation between market supply and demand.Few for the social inventory Estimation Study at present, and implement that the generaI investigation of 5,000,000 tame retail families, the whole nation is not had feasibility and economy at present.GeneraI investigation is to visit retail shop through manual work to carry out the data acquisition collection, utilizes manual calculation again, not only wastes the cost of great amount of manpower and time, money, and even more serious is that complicate statistics causes error easily, and then is difficult to draw statistics accurately.

Zero point, company was once through gathering 10000 tame retail families, the whole nation; Provided the social inventory estimated value of cigarette specification each province in every month; Its result is assert less than normal by the business personnel of market department; For example the social inventory of 2010 12 months China (firmly) maintains the 3000-6000 case, and estimated value is less than empirical value 2-3 ten thousand casees; Chinese cigarette sales company gathers social inventory, order volume and the retail price information at 3000 tame retail families, the whole nation at present weekly.For making full use of these information, social inventory is made more accurately and is estimated that need using more, the method for estimation of science satisfies the demands to cigarette.

Summary of the invention

The technical matters that the present invention will solve is to provide a kind of cigarette social inventory method of estimation of estimating based on hierarchical multiple regression, is used to improve the estimation degree of accuracy of existing cigarette social inventory.Thereby reach accurate production, satisfy the supply in cigarette market.

In order to solve the problems of the technologies described above, the present invention adopts following technical scheme: a kind of cigarette social inventory method of estimation of estimating based on hierarchical multiple regression, and this method may further comprise the steps:

1) adopt the method for stratified sampling to set up sample;

2) each layer is made the recurrence estimated value;

3) the recurrence estimated value of each layer that adds up, thus overall social inventory estimated value obtained.

Said step 2) computing method that return estimated value in adopt following formula:

${\stackrel{\‾}{y}}_{\mathrm{lr}}=\stackrel{\‾}{y}+\widehat{\mathrm{\β}}(\stackrel{\‾}{X}-\stackrel{\‾}{x}),$ $V\left({\stackrel{\‾}{y}}_{\mathrm{lr}}\right)=\frac{s_y^2-2\widehat{\mathrm{\β}}{s}_{\mathrm{xy}}+{\widehat{\mathrm{\β}}}^2{s}_x^2}{n}(1-\frac{n}{N})$

When $\widehat{\mathrm{\β}}=\frac{\mathrm{\Σ}(x_i-\stackrel{\‾}{x})(y_i-\stackrel{\‾}{y})}{\mathrm{\Σ}{(x_i-\stackrel{\‾}{x})}^2},$ $V{\left({\stackrel{\‾}{y}}_{\mathrm{Lr}}\right)}_{\mathrm{Min}}=\frac{s_y^2(1-{\mathrm{\ρ}}_{\mathrm{Xy}}^2)}{n}(1-\frac{n}{N})$

Wherein, N is a total number, and n is a sample drawn quantity,

Be the main variable population mean of investigating,

Be sample average, S is a population standard deviation, and s is a sample standard deviation,

Whole average for auxiliary variable;

Be sample average;

Be the estimator of x and y regression coefficient,

Be respectively homophony and look into the variance of variable y, auxiliary variable x and their covariance; ρ _XyBe the x of investigation sample and the related coefficient between the y;

Be the regression estimator result; Variance for estimator.

The add up recurrence estimated value of each layer of said step 3) may further comprise the steps:

A. according to the quantity of the StoreFront of each industry situation type of each province of calculated in advance, the recurrence estimated value of each industry situation type of weighted accumulation draws the social inventory estimator in each province;

B. the estimated value in each province of adding up is the overall social inventory estimated value in the whole nation.

The present invention relates to cigarette social inventory method of estimation through analysis to the retail sample data; And employing hierarchical multiple regression method of estimation; With the order volume in the sample data as auxiliary variable; Respectively the social inventory of each layer (province-industry situation type) is made and estimated to revise, the data estimator with each layer is aggregated into integral body then, obtains the cigarette social inventory estimated value of revised integral body.These sample survey methods of estimation make more science, credible of social inventory estimator.When other business data is made investigation, can make correction in conjunction with some auxiliary variables to estimated value through the data from the sample survey of small sample amount equally, the effect of getting twice the result with half the effort is arranged.

Description of drawings

Fig. 1 is a kind of cigarette social inventory of the present invention method of estimation process flow diagram.

Embodiment

Further specify embodiments of the invention below in conjunction with accompanying drawing.

The present invention provides a kind of cigarette social inventory method of estimation of estimating based on hierarchical multiple regression, and this method may further comprise the steps: adopt the method for stratified sampling to set up sample; Each layer is made the recurrence estimated value; The recurrence estimated value of each layer that adds up, thus overall social inventory estimated value obtained.

Stratified sampling was meant in when sampling, will totally be divided into mutual Uncrossed layer, then according to a certain percentage, extracted the individuality of some independently from each level, and the individuality that each level is taken out lumps together as sample.Stratified sampling utilizes the information of grasping in advance as far as possible, and has taken into full account the consistance that keeps the composition of sample and general structure, and this is very important to the representativeness that improves sample.When totally forming, often select the method for stratified sampling by several parts of obvious difference.

It is following that each layer made the concrete grammar that returns estimated value:

Hypothetical universe quantity is N, and sample drawn quantity is n, mainly investigates the variable population mean and does

Sample average does

Be the whole average of auxiliary variable, Be sample average; Be the estimator of x and y regression coefficient, Be respectively homophony and look into the variance of variable y, auxiliary variable x and their covariance; ρ _XyBe the x of investigation sample and the related coefficient between the y,

Be the regression estimator result; Use the variance of estimator

Come the evaluation prediction error size.

The computing method of regression estimator are following so:

${\stackrel{\‾}{y}}_{\mathrm{lr}}=\stackrel{\‾}{y}+\widehat{\mathrm{\β}}(\stackrel{\‾}{X}-\stackrel{\‾}{x}),$ $V\left({\stackrel{\‾}{y}}_{\mathrm{lr}}\right)=\frac{s_y^2-2\widehat{\mathrm{\β}}{s}_{\mathrm{xy}}+{\widehat{\mathrm{\β}}}^2{s}_x^2}{n}(1-\frac{n}{N})$

When $\widehat{\mathrm{\β}}=\frac{\mathrm{\Σ}(x_i-\stackrel{\‾}{x})(y_i-\stackrel{\‾}{y})}{\mathrm{\Σ}{(x_i-\stackrel{\‾}{x})}^2},$ $V{\left({\stackrel{\‾}{y}}_{\mathrm{Lr}}\right)}_{\mathrm{Min}}=\frac{s_y^2(1-{\mathrm{\ρ}}_{\mathrm{Xy}}^2)}{n}(1-\frac{n}{N})---\left(1\right)$

Contrast simple random sampling; Regression estimator must be superior to simple random sampling and ratio estimator; And

big more regression estimator effect is good more; Promptly search out the factor relevant more with estimating target, estimated accuracy is high more.The method also can expand to polynary factor

estimated.

The calculating of the hierarchical multiple regression estimator of cigarette social inventory, some steps below needing to divide:

A) to overall and sample layering

Mainly data are pressed province and industry situation type hierarchical.Shops's quantity of required each industry situation type of each province can obtain through the descending big-sample data statistics of State Bureau in later stage calculating.

B) each layer being made recurrence estimates

The target statistic of investigating is social inventory, with the order volume of sample data as auxiliary variable.The recurrence estimated value of can the branch following steps making each industry situation type of each province:

1) adds up the quantity of the shops of each industry situation type;

2) social inventory in the calculating retail sample data and the regression coefficient β between the order volume, wherein social inventory is a dependent variable, order volume is an independent variable;

3) calculate the average order volume x of average inventory level

sample of sample respectively, the mean value X of overall order volume;

4) with in the value substitution formula (1) that is calculated in the 3rd step, calculate the social inventory estimated value of each layer;

C) estimated value that gathers each layer is to overall

Through preceding two steps, can calculate the regression estimator of each industry situation type of each province, two steps below dividing gather:

1) according to the quantity of the StoreFront of each industry situation type of each province of calculated in advance, the recurrence estimated value of each industry situation type of weighted accumulation draws the social inventory estimator in each province;

2) the add up estimated value in each province is the overall social inventory estimated value in the whole nation;

D) national social inventory estimation effect

Social inventory to calculate 2010 the first weeks whole nation is estimated as example:

1) at first count shops's quantity of each industry situation type of each province, like following table:

2) calculate the regression coefficient

(using the linear regression module of SPSS Statistics software) in each province; Sample average population mean

etc., like following table (part):

3) through formula (1), calculate the average social inventory of the every kind of industry situation type in each province, and combine shops's number of each industry situation, calculate the social inventory total amount and estimate.Like following table (part):

4) data estimator is aggregated into the whole nation, obtains following result

Zhou Xulie	Whole nation social inventory (ten thousand casees)	Variance is estimated (bar square)
			1	3.77	3.04

The present invention relates to cigarette social inventory method of estimation through analysis to the retail sample data; And employing hierarchical multiple regression method of estimation; With the order volume in the sample data as auxiliary variable; Respectively the social inventory of each layer (province-industry situation type) is made and estimated to revise, the data estimator with each layer is aggregated into integral body then, obtains the cigarette social inventory estimated value of revised integral body.These sample survey methods of estimation make more science, credible of social inventory estimator.When other business data is made investigation, can make correction in conjunction with some auxiliary variables to estimated value through the data from the sample survey of small sample amount equally, the effect of getting twice the result with half the effort is arranged.

Above-mentioned description to embodiment is can understand and use the present invention for ease of the those of ordinary skill of this technical field.The personnel of skilled obviously can easily make various modifications to these embodiment, and needn't pass through performing creative labour being applied in the General Principle of this explanation among other embodiment.Therefore, the invention is not restricted to the embodiment here, those skilled in the art should be within protection scope of the present invention for improvement and modification that the present invention makes according to announcement of the present invention.

Claims (4)

1. cigarette social inventory method of estimation of estimating based on hierarchical multiple regression, it is characterized in that: this method may further comprise the steps:

1) adopt the method for stratified sampling to set up sample;

2) each layer is made the recurrence estimated value;

3) the recurrence estimated value of each layer that adds up, thus overall social inventory estimated value obtained.

2. a kind of cigarette social inventory method of estimation of estimating based on hierarchical multiple regression as claimed in claim 1 is characterized in that: said stratified sampling is meant data by province and the sampling of industry situation type hierarchical.

3. a kind of cigarette social inventory method of estimation of estimating based on hierarchical multiple regression as claimed in claim 1 is characterized in that: the computing method that return estimated value said step 2) adopt following formula:

${\stackrel{\‾}{y}}_{\mathrm{lr}}=\stackrel{\‾}{y}+\widehat{\mathrm{\β}}(\stackrel{\‾}{X}-\stackrel{\‾}{x}),$ $V\left({\stackrel{\‾}{y}}_{\mathrm{lr}}\right)=\frac{s_y^2-2\widehat{\mathrm{\β}}{s}_{\mathrm{xy}}+{\widehat{\mathrm{\β}}}^2{s}_x^2}{n}(1-\frac{n}{N})$

When $\widehat{\mathrm{\β}}=\frac{\mathrm{\Σ}(x_i-\stackrel{\‾}{x})(y_i-\stackrel{\‾}{y})}{\mathrm{\Σ}{(x_i-\stackrel{\‾}{x})}^2},$ $V{\left({\stackrel{\‾}{y}}_{\mathrm{Lr}}\right)}_{\mathrm{Min}}=\frac{s_y^2(1-{\mathrm{\ρ}}_{\mathrm{Xy}}^2)}{n}(1-\frac{n}{N})$

Wherein, N is a total number, and n is a sample drawn quantity, Be the main variable population mean of investigating, Be sample average, S is a population standard deviation, and s is a sample standard deviation,

Whole average for auxiliary variable;

Be sample average;

Be the estimator of x and y regression coefficient,

Be respectively homophony and look into the variance of variable y, auxiliary variable x and their covariance; ρ _XyBe the x of investigation sample and the related coefficient between the y;

Be the regression estimator result;

Variance for estimator.

4. a kind of cigarette social inventory method of estimation of estimating based on hierarchical multiple regression as claimed in claim 1 is characterized in that: the add up recurrence estimated value of each layer of said step 3) may further comprise the steps:

A. according to the quantity of the StoreFront of each industry situation type of each province of calculated in advance, the recurrence estimated value of each industry situation type of weighted accumulation draws the social inventory estimator in each province;

B. the estimated value in each province of adding up is the overall social inventory estimated value in the whole nation.

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