The Gamma distribution function Γ(α,β) is always used as a prior distribution density function of Bayesian exponential reliability growth model. Different value of α,β will make considerable difference in evaluating results.
For the data from multivariate t distribution, it is hard to do influence analysis based on its probability density function. But it can be considered as a particular Gaussian mixture by introducing the weight from the Gamma distribution.
Abstract In this paper, when prior distribution of the failure rate is in form of Gamma distribution Gamma(1,b), hierachical Bayesian estimation of the failure rate in exponential distribution has been come out from zero failure data.
In the paper,after introducing failure information,when prior distribution of failure rate is in form of Gamma distribution,hierarchical Bayesian estimation and synthesize hierarchical Bayesian estimation of thefailure rate in exponential distribution has come from zero failure data. Then the synthesize estimation of reliability of zero failure data is given.
In the paper it is proposed that, when prior distribution of failure rate is in form of Gamma distribution after introducing failure information, Hierarchical Bayesian estimation and synthesize Bayesian estimation of the failure rate in exponential distribution have come from zero failure data, and the synthesize estimation of reliablity of zeor failure data is given. And the calculation is performed regarding to practical problem.
A new estimate of shape parameter in the family of Gamma distribution
In this paper, a new estimator of the shape parameter in the family of Gamma distribution is constructed by using the moment idea, and it is proved that this estimator is strongly consistent and asymptotically normal.
Application of the theory of truncated probability distributions to studying minimal river runoff: Normal and gamma distribution
Content subscribing mechanism in P2P streaming based on gamma distribution prediction
From statistical regress, it was also found that the DSD follows the Gamma distribution best in most cases.
At present, the problem of determining the distribution function of Gamma distributed random variables's function, has not yet been well solved. But in the field of hydrologichydraulic calculation, we often have to deal with it. In this paper, on the basis of the basic probability theory, the joint distribution function of the sum and difference of two random variables, independent of each other and Gamma distributed, is developed in the form expressed by primary functions.
The author has constructed the squared error loss empirical Bayes estimations of location parameter about a class of gamma distributions and establi. shed their rates of convergence. It is noted that under suitable conditions these rates of convergence can be arbitrarily close to 1/2. An example which satisties the conditions of thc theorems in this paper is also given.
This paper deals with Bayes estimate of reliability growth for r/N (G) system based on binomial sampling. The survival probability R of the units possesses a priori negative logarithmic gamma-distributionor beta-distribution. The results corresponding to U (0. 1) or noninformetive prior situation can be deduced as special applications The important results are listed in theorem 2, 3 and 4.