K. R. Muraleedharan Nair

On characterizing the bivariate exponential and geometric distributions

In this note, a characterization of the Gumbels bivariate exponential distribution based on the properities of the conditional moments is discussed. The result forms a sort of bivariate analogue of the characterization of the univariate exponential distribution given by Sahobov and Geshev (1974) (cited in Lau and Rao ((1982), Sankhyā Ser. A, 44, 87)). A discrete version of the property provides a similar conclusion relating to a bivariate geometric distribution.

Bivariate Geometric Vitality Function and Some Characterization Results

Abtsrcat In the present work we extends the definition of geometric vitality function, considered by Nair and Rajesh (2000) to the bivariate set up. We also look into the problem of characterizing some bivariate models using the functional form of the bivariate geometric vitality function.

On Measures of Affinity for Truncated Distributions

Abstract: In the present paper we define affinity for truncated distributions and examine its properties. The relationship of this measure with other discrimination measures is examined. We also provide a characterization result for the proportional hazard model using the functional form of the truncated affinity. AMS (2000) Subject Classification: 62E10, 90B25

The New Zenga curve in the context of reliability analysis

ABSTRACT In this article, we look into the properties and characterizations of the New Zenga curve. The relationship of the curve with other measures of inequality as well as some reliability concepts are examined. Classification of lifetime distributions using the Zenga curve and an illustration for the behaviour of the curve using a survival data are also provided.

Nonparametric Estimation of the Geometric Vitality Function

Recently, Nair and Rajesh (2000) proposed a measure to describe the failure pattern of components/devices in terms of the geometric mean of the residual life. This measure find applications in modeling life time data. In the present work we provide a nonparametric kernel-type estimator for the geometric vitality function, both in the case of complete and censored samples. The properties of the estimator, under certain regularity conditions, are studied. The performance of the estimator is compared with the empirical estimator using a real data set and simulation studies are carried out using the Monte Carlo method.

Some Properties of Income Gap Ratio and Truncated GINI Coefficient

The income gap ratio and truncated Gini coefficients play an important role in the construction of poverty and affluence indices. In this paper we examine the question of determining the form of the income distributions based on the income gap ratio or truncated Gini coefficient for a given population and answer them in affirmative. We also discuss the behaviour of the Sen poverty index with respect to the head count ratio and the parameters of some selected income distribution models.

On a Class of Distributions Having Laplace Transforms with Multiple Negative Poles and Complex Zeros

In the present paper we look into certain properties of a class of probability density functions having Laplace transforms with multiple negative poles and complex zeros. Also characterization theorems are formulated for a mixture of gamma distributions in terms of zeros and poles in the Laplace transforms.