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Characterization of Some Multivariate Distributions
Nair, N.Unnikrishnan The Korean Statistical Society 1989 Journal of the Korean Statistical Society Vol.18 No.1
In this article the problem of characterizing multivariate distributions, possessing certain conditional distributions that have the same form as the parent model, are considered. It is shown that the forms of such conditional distributions characterize some well known distributions like the multivariate exponential, multivariate Burr, multivariate Lomax etc.
Reversed percentile residual life and related concepts
N. Unnikrishnan Nair,,B. Vineshkumar 한국통계학회 2011 Journal of the Korean Statistical Society Vol.40 No.1
In this work we discuss the properties of the reversed percentile residual life function and its relationship with the reversed hazard function. Some models with simple functional forms for both reversed hazard rate and reversed percentile residual life function are proposed. A method of distinguishing decreasing (increasing) reversed hazard rates (reversed percentile lives) is also presented.
Characterization of Some Continuous Distributionsby Properties of Partial Moments
B. Abraham,N. Unnikrishnan Nair,P. G. Sankaran 한국통계학회 2007 Journal of the Korean Statistical Society Vol.36 No.3
In this paper we present characterizations of the Pareto, Lomax, expo-nential and beta models by some properties of theirrth partial momentdened as r(t) = E[(X t)+ ]r, where (X t)+ = max(X t;0). Giventhe partial moments at a few truncation points, these results enable us tocalculate the moments at many other points.
Stochastic orders using quantile-based reliability functions
B. Vineshkumar,N. Unnikrishnan Nair,P. G. Sankaran 한국통계학회 2015 Journal of the Korean Statistical Society Vol.44 No.2
The concept of stochastic orders plays a major role in the theory and practice of statistics. It generally refers to a set of relations that may hold between a pair of distributions of random variables. In reliability theory, stochastic orders are employed to compare lifetime of two systems. In the present work, we develop new stochastic orders using the quantilebased reliability measures like the hazard quantile function and the mean residual quantile function. We also establish relationships among the proposed orders and certain existing orders. Various properties of the orders are also studied.
CHARACTERIZATION OF SOME CONTINUOUS DISTRIBUTIONS BY PROPERTIES OF PARTIAL MOMENTS
Abraham, B.,Nair, N. Unnikrishnan,Sankaran, P.G. The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.3
In this paper we present characterizations of the Pareto, Lomax, exponential and beta models by some properties of their $r^{th}$ partial moment defined as ${\alpha}_r(t)=E[(X-t)^+]^r$, where $(X-t)^+ = max(X-t,0)$. Given the partial moments at a few truncation points, these results enable us to calculate the moments at many other points.
Quantile based reliability aspects of partial moments
P. G. Sankaran,N. Unnikrishnan Nair,S.M. Sunoj 한국통계학회 2013 Journal of the Korean Statistical Society Vol.42 No.3
Partial moments are extensively used in literature for modeling and analysis of lifetime data. In this paper, we study properties of partial moments using quantile functions. The quantile based measure determines the underlying distribution uniquely. We then characterize certain lifetime quantile function models. The proposed measure provides alternate definitions for ageing criteria. Finally, we explore the utility of the measure to compare the characteristics of two lifetime distributions.
Some reliability properties of extropy for residual and past lifetime random variables
Krishnan Aswathy S.,Sunoj S. M.,Unnikrishnan Nair N. 한국통계학회 2020 Journal of the Korean Statistical Society Vol.49 No.2
In the present paper, we study the residual extropy using distribution function and quantile function approaches. We also investigate extropy in past lifetime in both approaches. Some characterizations and ageing properties of these extropy measures are proposed. Different stochastic orders based on the residual and past lifetime extropy are also presented.