Showing papers on "Natural exponential family published in 1978"
Book•
01 Jun 1978
TL;DR: In this article, the poisson process was used for characterisation of truncated distributions based on properties of order statistics, and multivariate exponential distributions for poisson processes were used.
Abstract: Preliminaries and basic results.- Characterizations based on truncated distributions.- Characterizations by properties of order statistics.- Characterizations of the poisson process.- Characterizations of multivariate exponential distributions.- Miscellaneous results.
90 citations
86 citations
TL;DR: In this paper, exponential polynomials are considered under the viewpoint of Nevanlinna theory and the fundamental properties and the asymptotic distribution of the zeros of these functions are discussed in detail.
Abstract: In this note exponential polynomials are considered under the viewpoint of the Nevanlinna theory. The fundamental properties and the asymptotic distribution of the zeros of these functions are discussed in detail. The results given by Polya and Schwengeler on exponential sums remain valid in the general case of exponential polynomials.
40 citations
38 citations
TL;DR: In this paper, the quartic exponential distribution defined by the probability density function of the type is examined in detail and the problem of obtaining maximum likelihood point estimates of the population parameters reduces to that of identifying the α as functions of population moments μ r ′, r = 1, 2.4.
Abstract: The quartic exponential (QE) distribution defined by the probability density function of the type is examined in detail. The problem of obtaining maximum likelihood point estimates of the population parameters reduces to that of identifying the α as functions of the population moments μ r ′, r = 1, 2.3.4. The invalidity is explained of methods proposed by previous authors to deal with the nonlinear relationships involved, and a new algorithm is developed which overcomes these objections. The new algorithm is applied to practical data, and the resulting distributions fitted to observed frequencies are shown to compare favourably with those obtained by previous Methods.
29 citations
19 citations
TL;DR: In this article, the integrability of empirical distribution functions was studied under various conditions on i>, [Xn], and (a] under various assumptions on [xn] and [a], where Xn is a sequence of vector valued random variables.
Abstract: If {Xn} is a sequence of vector valued random variables, {a„} a sequence of positive constants, and M = supn>l||(.Y, +. • • • + X„)/an\\\\, we examine when E($(M)) < oo under various conditions on i>, [Xn], and (a„). These integrability results easily apply to empirical distribution functions.
18 citations
15 citations
TL;DR: In this paper, the problem of estimating the parameter of an exponential distribution is described and techniques for constructing the estimates of this parameter and their confidence intervals under conditions of poor statistics are given.
14 citations
TL;DR: In this paper, some approximations, which are easily derivable from standard tables, are provided for the tolerance factors in one-sided β-content (guaranteed coverage) tolerance intervals.
Abstract: The problem of determining tolerance regions for the two parameter exponential family of distributions has been discussed recently by Aitchison and Dunsmore [l] and Guenther et al [3]. In this paper some approximations, which are easily derivable from standard tables, are provided for the tolerance factors in one-sided β-content (guaranteed coverage) tolerance intervals.
14 citations
TL;DR: In this paper, a new test was given and an asymptotic optimum property of the test was proved, which is based on the order statistics X[r1] and Y[1], where 1 r1n1 and 1 r2n2.
Abstract: Let X1., Xn1 and Y1., Yn1, be two independent random samples from exponential populations. The statistical problem is to test whether or not two exponential populations are the same, based on the order statistics X[1],.X[r1] and Y[1],.Y[rs] where 1 r1n1 and 1 r2n2. A new test is given and an asymptotic optimum property of the test is proved.
TL;DR: In this paper, necessary and sufficient conditions for admissibility of tests for a simple and a composite null hypotheses against one-sided alternatives on multivariate exponential distributions with discrete support are given.
Abstract: We state some necessary and sufficient conditions for admissibility of tests for a simple and a composite null hypotheses against ”one-sided” alternatives on multivariate exponential distributions with discrete support. Admissibility of the maximum likelihood test for “one –sided” alternatives and z χ2test for the independence hypothesis in r× scontingency tables is deduced among others.
01 Jul 1978
TL;DR: The general 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.
Abstract: : The general 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. 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. (Author)
TL;DR: In this paper, Miley et al. proposed a model of the process that incorporates the effect of rehabilitation when a person is no longer part of the high risk (i.e., high failure rate) population, but becomes a member of the (low risk) general population.
Abstract: e wish to thank Miley ( 1978) for his reanalysis of the data in our ~ ~ paper (Maltz and McCleary, 1977), for spotting the arithmetic errors in Table 2, and for his comments regarding the systematic change in the parameters as the observation time increases. There may be a number of explanations for this phenomenon. (1) When using grouped failure data (see Table I in Maltz and McCleary, 1977), it is often adequate to assume that all of the failures occurred at the end of the time period, which we did in the cited paper.2 One means of accounting for this &dquo;lumping&dquo; is to assume that all of the failures occurred in the middle of the time period. (This is mathematically equivalent to assuming that the failures are distributed uniformly throughout the time period.) One might also specifically account for this &dquo;lumping&dquo; by devising a model of the process that incorporates this effect. (2) When a person is rehabilitated he or she is no longer part of the high risk (i.e., high failure rate) population, but becomes a member of the (low-risk) general population. The model described in our previous article assumes that the failure rate of the low-risk population is
TL;DR: In this paper, the authors considered the probability distribution of the volume of a certain substance (e.g., river discharge, rainfall, deposites of clay, organism, etc.) that flows into a semi-infinite reservoir before its first emptiness for continuous and homogeneous input process when the substance is released at unit rate per unit of time.
Abstract: This paper considers the probability distribution of the volume of a certain substance (e.g. river discharge, rainfall, deposites of clay, organism, etc.) that flows into a semi-infinite reservoir before its first emptiness for continuous and homogeneous input process when the substance is released at unit rate per unit of time. A few moments of the distribution have been computed. A generalized gamma, and a generalized exponential distributions as particular cases are also discussed. Some possible applications of the generalized negative exponential distribution have been mentioned. These distributions are in fact the continuous analogues of the discrete LAGRANGE distributions recently considered by JAIN and others.
TL;DR: The purpose of this correction is to state precisely the class of distributions in which the exponential distribution is characterized and to prove certain amplifications as discussed by the authors, which is the same as the one in this paper.
Abstract: The purpose of this correction is to state precisely the class of distributions in which the exponential distribution is characterized and to prove certain amplifications.
TL;DR: In this paper, the normalized integral of a stationary process asymptotically approaches a Gaussian distribution, but the expectation of the exponential function of the unnormalized integral does not have the value anticipated from this fact.
Abstract: Appropriately restricted,the normalized integral of a stationary process asymptotically approaches a Gaussian distribution, but the expectation of the exponential function of the unnormalized integral does not have the value anticipated from this fact. An example is given, applicable to turbulence.
TL;DR: In this paper, a method of simulating a random variable with a standard exponential distribution is explained, a probability-theoretic justification of the method is given, and results of its computer realization are presented.
Abstract: A METHOD of simulating a random variable with a standard exponential distribution is explained. A probability-theoretic justification of the method is given, and results of its computer realization are presented.