256 research outputs found
Characterizations of probability distributions via bivariate regression of record values
Bairamov et al. (Aust N Z J Stat 47:543-547, 2005) characterize the
exponential distribution in terms of the regression of a function of a record
value with its adjacent record values as covariates. We extend these results to
the case of non-adjacent covariates. We also consider a more general setting
involving monotone transformations. As special cases, we present
characterizations involving weighted arithmetic, geometric, and harmonic means.Comment: accepted in Metrik
Characterizations of Pareto, Weibull and Power Function Distributions Based On Generalized Order Statistics
Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics
Characterizations of Certain Continuous Univariate Distributions Based on the Conditional Distribution of Generalized Order Statistics
The problem of characterizing probability distributions is an interesting problem which has recently attracted the attention of many researchers. Various characterization results have been established in different directions as reported in the literature. We present here, various characterizations of certain univariate continuous distributions based on the conditional distribution of generalized order statistics
Characterizations of Student's t-distribution via regressions of order statistics
Utilizing regression properties of order statistics, we characterize a family
of distributions introduced by Akhundov, Balakrishnan, and Nevzorov (2004),
that includes the t-distribution with two degrees of freedom as one of its
members. Then we extend this characterization result to t-distribution with
more than two degrees of freedom.Comment: To appear in "Statistics
New -empirical tests of symmetry based on extremal order statistics, and their efficiencies
We use a characterization of symmetry in terms of extremal order statistics
which enables to build several new nonparametric tests of symmetry. We discuss
their limiting distributions and calculate their local exact Bahadur efficiency
under location alternative which is mostly high.Comment: 17 page
Characterizations of Distributions via Conditional Expectation of Generalized Order Statistics
Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterizations of certain continuous distributions based on the conditional expectation of generalized order statistics
Characterizations of Levy Distribution via Sub-Independence of the Random Variables and Truncated Moments
The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Following Ahsanullah and Nevzorov (2014), we present certain characterizations of Levy distribution based on: (i) the sub-independence of the random variables; (ii) a simple relationship between two truncated moments; (iii) conditional expectation of certain function of the random variable. In case of independence, characterization (i) reduces to that of Ahsanullah and Nevzorov (2014)
Distributional Properties of Record Values of the Ratio of Independent Exponential and Gamma Random Variables
Both exponential and gamma distributions play pivotal roles in the study of records because of their wide applicability in the modeling and analysis of life time data in various fields of applied sciences. In this paper, a distribution of record values of the ratio of independent exponential and gamma random variables is presented. The expressions for the cumulative distribution functions, moments, hazard function and Shannon entropy have been derived. The maximum likelihood, method of moments and minimum variance linear unbiased estimators of the parameters, using record values and the expressions to calculate the best linear unbiased predictor of record values, are obtained
Estimation of the parameters of Exponential distribution using top-K-lists
This paper deals with the estimation of location and scale parameters of the exponential distribution based on top-k-list of a sequence of observations from a two parameter exponential distribution. The minimum variance unbiased estimates of the location and scale parameters are given. Some comparisons of the variances of these estimates with respect to that of the kth record values are given
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