On Concomitants of Order Statistics from Morgenstern Family

Scaria, Johny; Nair, N. Unnikrishnan

doi:10.1002/(sici)1521-4036(199907)41:4<483::aid-bimj483>3.0.co;2-2

Cited by 46 publications

(21 citation statements)

References 40 publications

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“…[12] derived the distribution of product and quotient of variates from Morgenstern type bivariate gamma distribution. [24] derived distribution of concomitant of order statistics arising from Morgenstern family. Estimation of parameters in Morgenstern type bivariate logistic, exponential and uniform distributions using ranked set sampling have been carried out by [4], [5] and [26] respectively.…”

Section: Introductionmentioning

confidence: 99%

Morgenstern type bivariate Lindley Distribution

Vaidyanathan

Varghese

2016

Stat., optim. inf. comput.

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In this paper, a bivariate Lindley distribution using Morgenstern approach is proposed which can be used for modeling bivariate life time data. Some characteristics of the distribution like moment generating function, joint moments, Pearson correlation coefficient, survival function, hazard rate function, mean residual life function, vitality function and stress-strength parameter R = P r(Y < X), are derived. The conditions under which the proposed distribution is an increasing (decreasing) failure rate distribution and positive (negative) quadrant dependent is discussed. Also, the method of estimating model parameters and stress-strength parameter by maximum likelihood is elucidated. Numerical illustration using simulated data is carried out to access the estimates in terms of mean squared error and relative absolute bias.Keywords Farlie-Gumbel-Morgenstern family, maximum likelihood estimation, mean residual life, mean squared error, positive quadrant dependence, relative absolute bias, stress-strength parameter, vector hazard rate, vitality function AMS 2010 subject classifications 60E05

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Section: Introductionmentioning

confidence: 99%

Morgenstern type bivariate Lindley Distribution

Vaidyanathan

Varghese

2016

Stat., optim. inf. comput.

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“…. , n. Then the pdf f [r:n] (y) of Y [r:n] and the joint pdf f [r,s:n] (y 1 , y 2 ) of Y [r:n] and Y [s:n] are given below (see [15]). For 1 ≤ r ≤ n, …”

Section: Estimation Of θ 2 Based On Complete Samplementioning

confidence: 99%

Estimation of parameter of Morgenstern type bivariate exponential distribution using concomitants of order statistics

Chacko

Thomas

2011

Statistical Methodology

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“…, n. Then clearly Y [r]r is distributed as the concomitant of rth order statistic of a random sample of n arising from (1). By using the expressions for means and variances of concomitants of order statistics arising from MTBED obtained by Scaria and Nair (1999), the mean and variance of Y [r]r for 1 ≤ r ≤ n are given below:…”

Section: Ranked Set Sample Mean As An Estimator Of θmentioning

confidence: 99%