A generalized bivariate exponential distribution

1967 ◽  
Vol 4 (2) ◽  
pp. 291-302 ◽  
Author(s):  
Albert W. Marshall ◽  
Ingram Olkin
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Residual Life ◽  
Waiting Times ◽  
Practical Importance ◽  
Moment Generating Function ◽  
Bivariate Exponential Distribution ◽  
Bivariate Exponential ◽  
Shock Models ◽  
Bivariate Poisson Process

In a previous paper (Marshall and Olkin (1966)) the authors have derived a multivariate exponential distribution from points of view designed to indicate the applicability of the distribution. Two of these derivations are based on “shock models” and one is based on the requirement that residual life is independent of age.The practical importance of the univariate exponential distribution is partially due to the fact that it governs waiting times in a Poisson process. In this paper, the distribution of joint waiting times in a bivariate Poisson process is investigated. There are several ways to define “joint waiting time”. Some of these lead to the bivariate exponential distribution previously obtained by the authors, but others lead to a generalization of it. This generalized bivariate exponential distribution is also derived from shock models. The moment generating function and other properties of the distribution are investigated.

A generalized bivariate exponential distribution

1967 ◽  
Vol 4 (02) ◽  
pp. 291-302 ◽  
Author(s):  
Albert W. Marshall ◽  
Ingram Olkin
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Residual Life ◽  
Waiting Times ◽  
Practical Importance ◽  
Moment Generating Function ◽  
Bivariate Exponential Distribution ◽  
Bivariate Exponential ◽  
Shock Models ◽  
Bivariate Poisson Process

In a previous paper (Marshall and Olkin (1966)) the authors have derived a multivariate exponential distribution from points of view designed to indicate the applicability of the distribution. Two of these derivations are based on “shock models” and one is based on the requirement that residual life is independent of age. The practical importance of the univariate exponential distribution is partially due to the fact that it governs waiting times in a Poisson process. In this paper, the distribution of joint waiting times in a bivariate Poisson process is investigated. There are several ways to define “joint waiting time”. Some of these lead to the bivariate exponential distribution previously obtained by the authors, but others lead to a generalization of it. This generalized bivariate exponential distribution is also derived from shock models. The moment generating function and other properties of the distribution are investigated.

BLOCK AND BASU'S BIVARIATE EXPONENTIAL DISTRIBUTION WITH APPLICATION TO DROUGHT DATA

2006 ◽  
Vol 21 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Exponential Distribution ◽  
Bivariate Exponential Distribution ◽  
Bivariate Exponential ◽  
Exact Distributions ◽  
Hydrological Applications

Motivated by hydrological applications, the exact distributions ofR=X+Y,P=XY, andW=X/(X+Y) and the corresponding moment properties are derived whenXandYfollow Block and Basu's bivariate exponential distribution. An application of the results is provided to drought data from Nebraska.

Predicting the Duration of Manufacturing Process with Two Complement Materials

2016 ◽  
Vol 709 ◽  
pp. 46-50
Author(s):  
Hui Hsin Huang
Keyword(s):  
Exponential Distribution ◽  
Future Study ◽  
Manufacturing Process ◽  
Bivariate Exponential Distribution ◽  
Moment Methods ◽  
Bivariate Exponential ◽  
The Future ◽  
Production Demand

In the marketing, there are some correlated between two complement materials when predicting the duration of manufacturing process. Two different kinds of materials are complementary if using more of one material requires the use of more of another. Thus, based on this view of point, when we estimate the production demand quantity, we can’t consider these two durations of manufacturing process as dependent. In this paper we propose the bivariate exponential distribution to model two related manufacturing durations of two complement materials. Finally, we demonstrate both MLE and moment methods to estimate the parameters of our model. This can provide the reference for the future study to choice a suitable estimation.

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