Morgenstern type bivariate Lindley Distribution

Abstract

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

A Bayesian Inference Approach for Bivariate Weibull Distributions Derived from Roy and Morgenstern Methods

“…where S w (•) is given in (11). According to [63], a primary limitation of the definition for the hazard function defined according to Basu's definition is that this function is defined from R 2 → R, that is, h(x, y) is not a vector quantity. To overcome this limitation, [27] defined the bivariate hazard rate function in vector form as follows, Assuming the BW-Type M distribution, the vector components of the joint hazard rate function are given by,…”

A new cure rate regression framework for bivariate data based on the Chen distribution

“…According to Vaidyanathan et al, 25 the primary limitation of the definition for the traditional hazard function in the bivariate case is that this function is defined from R 2 false→ double-struckR, that is, h false( x , y false) is not a vector quantity. To overcome this limitation, Johnson and Kotz 26 defined the bivariate hazard rate function in vector form based on the derivative of the logarithm of the joint survival function.…”

Discriminating Between Exponential and Lindley Distributions

“…This data set consists of waiting time in minutes of 100 customers in a bank (Ghitany et al [2]). For this data set, MLEs are calculated using (6) Since T < 0, Lindley distribution can be used to model the data. To calculate PCS value, 1000 bootstrap samples are generated from the data and the estimated PCS is obtained as 0.8009.…”

“…Some generalizations and modifications of Lindley distribution have been suggested by Zakerzadeh and Dolati [3], Nadarajah et al [4], Bakouch et al [5], Vaidyanathan and Sharon Varghese [6]. Krishna and Kumar [7], Mazucheli and Achcar [8], Al-Mutairi et al [9] have studied applications of Lindley distribution in analyzing lifetime data.…”