Sales distribution of consumer electronics

Hisano, Ryohei; Mizuno, Takayuki

doi:10.1016/j.physa.2010.09.033

Cited by 13 publications

(21 citation statements)

References 21 publications

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“…However, this calculation still suggests a way to reconcile the different empirical estimates of power-law exponents for tangible fixed assets, the number of workers, and annual sales. See Mizuno et al (2011) for more empirical results and discussion along this line of research.…”

Section: Resultsmentioning

confidence: 99%

A New Method for Measuring Tail Exponents of Firm Size Distributions

et al. 2011

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The authors propose a new method for estimating the power-law exponents of firm size variables. Their focus is on how to empirically identify a range in which a firm size variable follows a power-law distribution. On the one hand, as is well known a firm size variable follows a power-law distribution only beyond some threshold. On the other hand, in almost all empirical exercises, the right end part of a distribution deviates from a power-law due to finite size effects. The authors modify the method proposed by Malevergne et al. (2011). In this way they can identify both the lower and the upper thresholds and then estimate the power-law exponent using observations only in the range defined by the two thresholds. They apply this new method to various firm size variables, including annual sales, the number of workers, and tangible fixed assets for firms in more than thirty countries. Special Issue New Approaches in Quantitative Modeling of Financial MarketsJEL C16, C18, D20, E23

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Section: Resultsmentioning

confidence: 99%

A New Method for Measuring Tail Exponents of Firm Size Distributions

et al. 2011

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“…Market share was defined by the daily sales volume of a generic product such as "digital camera", "mouse", and so on. Note also that to keep consistency with Hisano and Mizuno [31], we only analyzed products which are "alive" by the definition described below when analyzing market share distributions. Products shown in Fig.…”

Section: Validation Of the Model Assumptionsmentioning

confidence: 99%

“…Hisano and Mizuno [31] analyzed the same data set and reported that the asymptotic behavior of the market The lower threshold for the validity of the power law tail of the distribution was estimated using the method described in Ref. [31].…”

Section: Tests Of the Theoreticalmentioning

confidence: 99%

Predicted and verified deviations from Zipf’s law in ecology of competing products

2011

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Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations that remain unexplained. A recently developed theory finds that the interplay between (i) one of the most universal ingredients, namely stochastic proportional growth, and (ii) birth and death processes, leads to a generic power-law distribution with an exponent that depends on the characteristics of each ingredient. Here, we report the first complete empirical test of the theory and its application, based on the empirical analysis of the dynamics of market shares in the product market. We estimate directly the average growth rate of market shares and its standard deviation, the birth rates and the "death" (hazard) rate of products. We find that temporal variations and product differences of the observed power-law exponents can be fully captured by the theory with no adjustable parameters. Our results can be generalized to many systems for which the statistical properties revealed by power law exponents are directly linked to the underlying generating mechanism. Power-law distributions constitute ubiquitous statistical features of many natural and social complex phenomena [1][2][3]. The probability distribution function p(s) of a random variable,describes a particularly slow decay with s of the probability p(s)ds that the random variable is found in one realization between s and s + ds. A power-law distribution is such that any of its moment of order q larger than the power-law exponent µ is mathematically infinite. Among power-law distributions, Zipf's law, corresponding to µ = 1, has been proposed as a fundamental characteristic for many systems [4-6]. Zipf's law implies that we no longer have finite means in infinite systems, or that the means are strongly system size dependent in the real world. Motivated by its apparent ubiquity and interesting features, many efforts have been made to attempt explaining the existence of power-law distributions. One of the general mechanisms to generate power-law distributions is embodied in the multiplicative stochastic growth models, having Gibrat's rule of proportional growth [7] as a key ingredient. Expressed in continuous time, Gibrat's rule is equivalent to the well known geometric Brownian motionwhere r denotes a drift, σ is the volatility (or standard deviation) and W (t) is a standard Wiener process. However, Gibrat's rule alone cannot generate a stable powerlaw distribution, since the solution of the process (2) leads to a non-stationary log-normal distribution. Since Herbert Simon's work [8][9][10] that extended previous attempts at explaining Zipf's law [4,[11][12][13]], a huge literature followed that is spread across a variety of disciplines [14][15][16][17][18][19][20][21][22][23]. This has led to the understanding that an apparently minor modification in the multiplicative process applying just when S(t) becomes small suffice...

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“…Chevalier and Goolsbee (2003) used a power law function to describe online books sales, while Hisano and Mizuno (2011) observed that the sales distribution of consumer electronics follows both power law and log-normal distributions. Stanley et al (1995) used a log-normal distribution to fit the size distribution of firms.…”

Section: Introductionmentioning

confidence: 99%

Estimating sales and sales market share from sales rank data for consumer appliances

Touzani

Buskirk

2016

Physica A: Statistical Mechanics and its Applications

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Our motivation in this work is to find an adequate probability distribution to fit sales volumes of different appliances. This distribution allows for the translation of sales rank into sales volume. This paper shows that the log-normal distribution and specifically the truncated version are well suited for this purpose. We demonstrate that using sales proxies derived from a calibrated truncated log-normal distribution function can be used to produce realistic estimates of market average product prices, and product attributes. We show that the market averages calculated with the sales proxies derived from the calibrated, truncated log-normal distribution provide better market average estimates than sales proxies estimated with simpler distribution functions.4

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Sales distribution of consumer electronics

Cited by 13 publications

References 21 publications

A New Method for Measuring Tail Exponents of Firm Size Distributions

A New Method for Measuring Tail Exponents of Firm Size Distributions

Predicted and verified deviations from Zipf’s law in ecology of competing products

Estimating sales and sales market share from sales rank data for consumer appliances

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