Characterizations of Certain Continuous Univariate Distributions Based on the Conditional Distribution of Generalized Order Statistics (original) (raw)
Related papers
Characterization of distributions by conditional expectation of generalized order statistics
Statistical Papers, 2008
In this work, general forms of many well-known continuous probability distributions are characterized by conditional expectation of some functions of generalized order statistics. These results are the generalization of the characterization results based on conditional expectation of the functions of order statistics given by Khan and Abu-Salih (1989).
Communications in Statistics - Theory and Methods, 2013
Nanda (2010) and Bhattacharjee et al. (2013) characterized a few distributions with help of the failure rate, mean residual, log-odds rate and aging intensity functions. In this paper, we generalize their results and characterize some distributions through functions used by them and Glaser's function. Kundu and Ghosh (2016) obtained similar results using reversed hazard rate, expected inactivity time and reversed aging intensity functions. We also, via w(•)-function defined by Cacoullos and Papathanasiou (1989), characterize exponential and logistic distributions, as well as Type 3 extreme value distribution and obtain bounds for the expected values of selected functions in reliability theory. Moreover, a bound for the varentropy of random variable X is provided.
Let X(1;n;m;k);X(2;n;m;k);:::;X(n;n;m;k) be n generalized order statis- tics from an absolutely continuous (with respect to Lebesgue measure) distribution. We give characterizations of distributions by means of Efˆ(X(s;n;m;k))jX(r;n;m;k) = xg = g(x) and Efˆ(X(r;n;m;k))jX(s;n;m;k) = xg = g(x);s > r under some mild conditions on ˆ(:) and g(:). It is shown that most of the known characteri- zation results based on conditional expectations are special cases of the results of this paper. 1. Introduction. Let X1;X2;:::Xn be a random sample of size n from an absolutely continuous (with respect to Lebesgue measure) distribution function (df) F(x) and the corresponding probability distribution function (pdf) f(x). We will take the support of F(x) = (fi;fl); where fi = inffx 2 IR; F(x) > 0g and fl = supfx 2 IR; F(x) < 1g: Ferguson (1967) introduced the characterization of distributions based on the linearity of regression of adjacent order statistics E(Xr+1;njXr;n = x) and its dual E...
Characterization of Continuous Distributions Based on Order Statistics
Journal of computational & theoretical statistics, 2015
A family of continuous probability distributions ,) () (b x ah x F ) , ( x have been characterized through conditional expectation of power of difference of two order statistics, conditioned on a pair of non-adjacent order statistics. The characterization results presented in this paper extend some of the existing results based on the order statistics. Further, some particular cases and examples are also discussed.
Characterizations via regression of generalized order statistics
Statistical Methodology, 2013
In this paper, we present some characterizations of distributions based on the regression of generalized order statistics. In the case of adjacent generalized order statistics, the conditional expectation of one generalized order statistic given the other one completely characterizes distributions depending on the type of regression function. In the case of non-adjacent generalized order statistics, the characterization of distributions using conditional expectations becomes more complicated. The results presented in the paper unify and extend some of the existing results involving order statistics and record values.
Communications in Statistics - Theory and Methods, 2007
For a general class of distributions some characterizations through the properties of conditional expectations of order statistics and progressively Type-II censored order statistics are given. Let X 1 n X 2 n X n n be the order statistics of the sample X 1 X 2 X n from a continuous distribution and X R 1 m n X R 2 m n X R m m n be the progressively Type-II censored order statistics with the progressively Type-II censoring scheme R = R R R. We show that in this case, the joint distribution of X R 1 m n X R m m n can be reduced to the joint distribution of usual order statistics of a sample size m from a continuous random variable.