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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.
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.