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Ronghua Wang, Beiqing Gu. STATISTICAL ANALYSIS TECHNIQUE OF TWO-PARAMETER GENERALIZED EXPONENTIAL SUM DISTRIBUTION[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 346-371. doi: 10.11948/2017023

Citation:

Ronghua Wang, Beiqing Gu. STATISTICAL ANALYSIS TECHNIQUE OF TWO-PARAMETER GENERALIZED EXPONENTIAL SUM DISTRIBUTION[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 346-371. doi: 10.11948/2017023

STATISTICAL ANALYSIS TECHNIQUE OF TWO-PARAMETER GENERALIZED EXPONENTIAL SUM DISTRIBUTION

Ronghua Wang¹,
Beiqing Gu²

1 Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China;
2 School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China

Fund Project:

Abstract

Abstract

A new life distribution is proposed, known as "two-parameter generalized exponential sum distribution". We study the density function and failure rate function, the average failure rate function, the image features and the numerical characteristics of the mean residual life of the distribution. Several methods of calculating point estimation of parameters are discussed. Through the Monte-Carlo simulation, we compare the precision of the point estimations. In our opinion, the best linear unbiased estimation is the most optimal solution of these methods. At the same time, several methods of calculating parameters of interval estimations are given. We also discuss the precision of interval estimations by Monte-Carlo simulation and use the best linear unbiased estimation and the best linear invariant estimation to construct interval estimations which are better than other estimation method. Finally, several simulation examples and a case of maintaining tanks is used to illustrate the application of the methods presented in this paper.
- Two-parameter generalized exponential sum distribution /
- threeparameter generalized exponential sum distribution /
- exponential sum distribution /
- image feature /
- numerical characteristics /
- point estimation /
- interval estimation /
- Monte-Carlo simulation
MSC: 62N05

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