Exponential distributions are characterized by distributional properties of generalized order statistics. These characterizations include known results for ordinary order statistics and record values as particular cases.
Conditions under which the solutions of a partial difference equations system can be probability functions are examined.When the coefficients of the system are polynomials then the partial difference equations system satisfied by generating functions associated to these distributions are easily obtained; they give useful recurrence relations for the moments. Three examples are given as well.
In survival studies and life testing, the data are generally truncated. Recently, authors have studied a weighted version of Kerridge inaccuracy measure for truncated distributions. In the present paper we consider weighted residual and weighted past inaccuracy measure and study various aspects of their bounds. Characterizations of several important continuous distributions are provided based on weighted residual (past) inaccuracy measure.
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 -function defined by Cacoullos and Papathanasiou...
We give characterizations of the uniform distribution in terms of moments of order statistics when the sample size is random. Special cases of a random sample size (logarithmic series, geometrical, binomial, negative binomial, and Poisson distribution) are also considered.
-3Properties of spacings of generalized order statistics based on IFR and DFR distributions are shown to characterize exponential distributions.
Power distributions can be characterized by equalities involving three moments of order statistics. Similar equalities involving three moments of k-record values can also be used for such a characterization. The case of samples with random sizes is also considered.
Two characterizations of the exponential distribution among distributions with support the nonnegative real axis are presented. The characterizations are based on certain properties of the characteristic function of the exponential random variable. Counterexamples concerning more general possible versions of the characterizations are given.
We give characterization conditions for the inverse Weibull distribution and generalized extreme value distributions by moments of kth record values.
We characterize uniform and exponential distributions via moments of the kth record statistics. Too and Lin's (1989) results are contained in our approach.
For any orthogonal multi-way classification, the sums of squares appearing in the analysis of variance may be expressed by the standard quadratic forms involving only squares of the marginal and total sums of observations. In this case the forms are independent and nonnegative definite. We characterize all two-way classifications preserving these properties for some and for all of the standard quadratic forms.
In this paper we give a characterization of the multivariate normal distribution through the conditional distributions in the most general case, which include the singular distribution.