2949775109

Hacettepe Journal of Mathematics and Statistics Yolume 44(3) (2015), 715-733

Exact moments of generalized order statistics from type II exponentiated log-logistic distribution

Devendra Kumar *

Abstract

In this paper some new simple expressions for single and product moments of generalized order statistics from type II exponentiated log-logistic distribution have been obtained. The results for order statistics and record values are deduced from the relations derived and some ra-tio and inverse moments of generalized order statistics are also carried out. Further, a characterization result of this distribution by using the conditional expectation of generalized order statistics is discussed.

2000 AMS Classification: 62G30, 62E10.

Keywords:    Exact moments, ratio and inverse moments, generalized order sta

tistics, order statistics, upper record values, type II exponentiated log-logistic distribution and characterization.

Received 07/11/2013 : Accepted 29/06/2014 Doi : 10.15672/HJMS.2014217472

1. Introduction

A random variable X is said to have type II exponentiated log-logistic distribution if its probability density function (pdf) is given by

/(*) =

af3(x/a)⁰ 1 <r[l + (x/cr)^]^Q+¹

x > 0, a, a > 0,    > 1

(i.i)

and the corresponding survival function is

(1.2)

x > 0, a, cr > 0, 0 > 1.

It is easy to see that

afiF(x) = cr[l + (x/a)⁰]xf{x).    (1.3)

Log-logistic distribution is considered as a special case of type II exponentiated log-logistic distribution when a = 1. It is used in survival analysis as a parametric model where in the mortality ratę first increases then decreases, for example in cancer diagnosis

‘Department of Statistics, Amity Institute of Applied Sciences Amity University, Noida-201 303, India

Email: devendrastats@gmail. com