Showing papers on "Natural exponential family published in 1980"
TL;DR: The authors considered procedures for combining individual probability distributions that belong to some "family" into a "group" probability distribution that belongs to the same family, and applied these results to models of reaction time in psychological experiments.
87 citations
TL;DR: In this paper, a class of multivariate distributions which is an extension of the class of univariate distributions with increasing failure rate averages is introduced and properties of this class are studied.
Abstract: A class of multivariate distributions which is an extension of the class of univariate distributions with increasing failure rate averages is introduced. Properties of this class are studied and examples of distributions which are members of this class are given.
53 citations
TL;DR: In this paper, the Blackwell-Rao and Lehmann-Scheffe theorems are used to derive the minimum variance unbiased estimator for the two-parameter exponential distribution.
Abstract: In this paper the Blackwell-Rao and Lehmann-Scheffe theorems are used to derive the minimum variance unbiased estimator ofP=Pr{Y
40 citations
TL;DR: In this article, given a type 2 censored sample from a left truncated exponential distribution, Bayesian prediction bounds for future observations and the uncensored sample observations were derived for both classical and Bayesian approaches.
Abstract: Given a type 2 censored sample from a left truncated exponential distribution, Bayesian prediction bounds are derived for future observations and the uncensored sample observations. Numerical examples are used to compare these bounds with those obtained using both classical and Bayesian approaches assuming the lifetimes follow a two-parameter exponential distribution.
36 citations
30 citations
TL;DR: In this article, an algorithm for the computation of the exponential function of real argument is presented, with no restrictions on the range of the argument or on the precision that may be demanded in the results.
Abstract: An algorithm is presented for the computation of the exponential function of real argument. There are no restrictions on the range of the argument or on the precision that may be demanded in the results.
18 citations
18 citations
TL;DR: In this article, two characterizations of the exponential distribution are discussed, based on a generalization of the lack of memory property, motivated by the notion of relevance of distributions introduced by Krakowski (1973).
Abstract: : In this note two characterizations of the exponential distribution are discussed, based on a generalization of the lack of memory property. These results were motivated by the notion of 'relevation of distributions' introduced by Krakowski (1973). (Author)
16 citations
TL;DR: The exact distribution of the likelihood ratio statistic for testing the equality of p one-parameter exponential populations is obtained in a computational form as mentioned in this paper, where tables of 5% and 1% significance points are given for p = 3(1)6.
Abstract: The exact distribution of the likelihood ratio statistic for testing the equality of p one-parameter exponential populations is obtained in a computational form. Tables of 5% and 1% significance points are given for p =3(1)6. An asymptotic expansion in terms of a beta distribution is also given.
15 citations
TL;DR: In this article, the work of Weier & Basu (1980) is extended to a special case of the trivariate exponential distributions and to the general k-variate case.
Abstract: Summary
In this paper the work of Weier & Basu (1980) is extended to a special case of the trivariate exponential distributions and to the general k-variate case. In the trivariate case several statistics are derived including one based on the likelihood ratio approach and the locally most powerful rank statistic, and power studies are carried out. The general k-variate model is derived, and testing for independence is shown to reduce to a solved problem.
8 citations
TL;DR: The well known acceptance/rejection algorithm for generating random values on a computer is specialized for distribution tails using an exponential majorizing function and a linear minorizing function, which becomes particularly efficient.
Abstract: The well known acceptance/rejection algorithm for generating random values on a computer is specialized for distribution tails. Using an exponential majorizing function and a linear minorizing function, the tail algorithm becomes particularly efficient. Specific algorithms are given for the normal, gamma, Weibull and beta distributions. While the algorithms can be used alone, it is anticipated that their major value will be to serve as components of algorithms for complete distributions.
01 Mar 1980
TL;DR: In this article, a first-order stochastic difference equation with random coefficients is shown to have a solution which makes the marginal distribution of the stationary sequence generated by the equation a convex mixture of two exponential distributions.
Abstract: : A first-order stochastic difference equation with random coefficients is shown to have a solution which makes the marginal distribution of the stationary sequence generated by the equation a convex mixture of two exponential distributions. This Markovian process should be broadly applicable in stochastic modelling in operations analysis. Moreover it can be extended quite simply to a mixed exponential process with mixed pth-order autoregressive and qth-order moving average correlation structure. Coupling of the processes to model multivariate situations is also discussed. (Author)
TL;DR: In this article, a characterization of exponential distributions based on the properties of linear transformations of order statistics is presented. But this characterization is restricted to the case where the distribution of linear combinations of the order statistics from exponential distributions is linear.
Abstract: This note contains a characterization of exponential distributions based on the properties of linear transformations of order statistics. This is a certain converse of a well known theorem of Renyi about the distribution of linear combinations of order statistics from exponential distributions. Some statistical applications of the result are indicated.
01 Jan 1980
TL;DR: In this article, the problem of estimating the parameter v when an information described above is accessible at random moments of time is considered, where the loss incurred by the statistician in estimating v is not only due to the error of estimation but also to the cost of observation.
Abstract: Let X1,..., Xn be independent random variables with the same probability distribution depending on an unknown parameter v . Suppose that Xi,i=1,...,n is observed at time ti, where 0 ≤ t1 ≤ t2 ≤ ... ≤ tn, and t1,..., tn are independent of X1,...,Xn.We will, in fact, suppose that t1,...,tn are the order statistics of positive exchangeable random variables U1,...,Un which are independent of X1,...,Xn. We shall be interested in the problem of estimating the parameter v when an information es described above is accessible at random moments of time. We assume that the loss incurred by the statistician in estimating v is not only due to the error of estimation but also to the cost of observation.
TL;DR: In this paper, a multistage procedure is developed to determine t≦k groups such that in any one group the distributions have μi's that are not appreciably different.
Abstract: Suppose we have k random samples each of size n from a two parameter exponential distribution with location parameters μ i i=1,…,k, and where each item has the same, unknown scale parameter. A multistage procedure is developed to determine t≦k groups such that in any one group the distributions have μi's that are not appreciably different. The method yields a unique grouping and extends the approach of the Kumar and Pate1 test.The emphasis is on the development of a procedure based on the null sampling distribution of the maximum gap of the ordered first order statistics from exponential distributions. The procedure is based on complete ordered samples or censored (of any or of all) samples.