S. Baratpour

Bio: S. Baratpour is an academic researcher from Ferdowsi University of Mashhad. The author has contributed to research in topics: Order statistic & Maximum entropy probability distribution. The author has an hindex of 11, co-authored 20 publications receiving 454 citations.

Testing Goodness-of-Fit for Exponential Distribution Based on Cumulative Residual Entropy

Abstract: Testing exponentiality has long been an interesting issue in statistical inferences. In this article, we introduce a new measure of distance between two distributions that is similar Kullback–Leibler divergence, but using the distribution function rather than the density function. This new measure is based on the cumulative residual entropy. Based on this new measure, a consistent test statistic for testing the hypothesis of exponentiality against some alternatives is developed. Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for the test statistics. Also, by means of Monte Carlo simulations, the power of the proposed test under various alternative is compared with that of other tests. Finally, we found that the power differences between the proposed test and other tests are not remarkable. The use of the proposed test is shown in an illustrative example.

Characterizations based on Rényi entropy of order statistics and record values

Abstract: Two different distributions may have equal Renyi entropy; thus a distribution cannot be identified by its Renyi entropy. In this paper, we explore properties of the Renyi entropy of order statistics. Several characterizations are established based on the Renyi entropy of order statistics and record values. These include characterizations of a distribution on the basis of the differences between Renyi entropies of sequences of order statistics and the parent distribution.

Entropy properties of record statistics

Abstract: Record values can be viewed as order statistics from a sample whose size is determined by the values and the order of occurrence of observations. They are closely connected with the occurrence times of a corresponding non-homogenous Poisson process and reliability theory. In this paper, the information properties of record values are presented based on Shannon information. Several upper and lower bounds for the entropy of record values are obtained. It is shown that, the mutual information between record values is distribution free and is computable using the distribution of the record values of the sequence from the uniform distribution.

Some characterizations based on entropy of order statistics and record values

Abstract: In the literature of information theory, Shannon entropy plays an important role and in the context of reliability theory, order statistics and record values are used for statistical modeling. The aim of this article is characterizing the parent distributions based on Shannon entropy of order statistics and record values. It is shown that the equality of the Shannon information in order statistics or record values can determine uniquely the parent distribution. The exponential distribution is characterized through maximizing Shannon entropy of record values under some constraints. The results are useful in the modeling problems.

On weighted cumulative residual entropy

Abstract: In analogy with the weighted Shannon entropy proposed by Belis and Guiasu (1968) and Guiasu (1986), we introduce a new information measure called weighted cumulative residual entropy (WCRE). This is based on the cumulative residual entropy (CRE), which is introduced by Rao et al. (2004). This new information measure is “length-biased” shift dependent that assigns larger weights to larger values of random variable. The properties of WCRE and a formula relating WCRE and weighted Shannon entropy are given. Related studies of reliability theory is covered. Our results include inequalities and various bounds to the WCRE. Conditional WCRE and some of its properties are discussed. The empirical WCRE is proposed to estimate this new information measure. Finally, strong consistency and central limit theorem are provided.

On families of beta- and generalized gamma-generated distributions and associated inference

Abstract: A general family of univariate distributions generated by beta random variables, proposed by Jones, has been discussed recently in the literature. This family of distributions possesses great flexibility while fitting symmetric as well as skewed models with varying tail weights. In a similar vein, we define here a family of univariate distributions generated by Stacy’s generalized gamma variables. For these two families of univariate distributions, we discuss maximum entropy characterizations under suitable constraints. Based on these characterizations, an expected ratio of quantile densities is proposed for the discrimination of members of these two broad families of distributions. Several special cases of these results are then highlighted. An alternative to the usual method of moments is also proposed for the estimation of the parameters, and the form of these estimators is particularly amenable to these two families of distributions.

Probability A Graduate Course

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Generalized cumulative residual entropy and record values

Abstract: The Shannon entropy of a random variable has become a very useful tool in Probability Theory. In this paper we extend the concept of cumulative residual entropy introduced by Rao et al. (in IEEE Trans Inf Theory 50:1220–1228, 2004). The new concept called generalized cumulative residual entropy (GCRE) is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. We also consider a dynamic GCRE obtained using the residual lifetime. For these concepts we obtain some characterization results, stochastic ordering and aging classes properties and some relationships with other entropy concepts.

The extropy of order statistics and record values

Abstract: Characterization results, monotone properties and lower bounds of extropy of order statistics and record values are studied. We also investigate the symmetric properties of extropy of order statistics.

The residual extropy of order statistics

Abstract: Residual extropy was proposed to measure residual uncertainty of a random variable. Monotone properties and characterization results of this measure were studied. Similar properties of the proposed measure of order statistics were also discussed.