Showing papers on "Natural exponential family published in 1981"
84 citations
TL;DR: In this article, three different estimators for Pr(X < Y) when X and Y have a bivariate exponential distribution are provided, and the asymptotic variances of the three estimators are also derived.
Abstract: This paper provides three different estimators for Pr(X < Y) when X and Y have a bivariate exponential distribution. The asymptotic variances of the three estimators are also derived. A test for the equality of the means of X and Y and confidence limits for the difference of the two means are presented. Our results are directly applicable in a reliability context with underlying bivariate exponential distribution.
76 citations
TL;DR: In this article, general limit theorems for functions of sum-type for such random vectors are obtained; simple sums, linear combinations, $m$-dependent sums, and $U$-statistics are considered.
Abstract: Consider a sample from a $p$-dimensional exponential family and a random vector whose distribution is the same as that of the sample given a sufficient statistic. General limit theorems for functions of sum-type for such random vectors are obtained; simple sums, linear combinations, $m$-dependent sums, and $U$-statistics are considered. The results are illustrated by some examples.
56 citations
TL;DR: In this article, the reliability function R = P(X less than Y) has been estimated when X and Y follow gamma, exponential or bivariate exponential distributions, and it has been shown that R is a function of the distribution.
Abstract: : In this paper the reliability function R = P(X less than Y) has been estimated when X and Y follow gamma, exponential or bivariate exponential distributions. The paper is partly expository. (Author)
50 citations
TL;DR: In this article, a method of estimating exponential survival distributions where the expected survival time is linear in several independent variables is presented, and a modification, applying the exponential cumulative distribution function, is made to handle data where not all individuals have an observed time of death.
39 citations
TL;DR: In this article, conditional exponential families of Markov processes are defined and a representation of the score function martingale is established for the important conditionally additive case, which unifies those obtained separately for different examples and provides the key to asymptotic normality results for the maximum likelihood estimate.
Abstract: Conditional exponential families of Markov processes are defined and a representation of the score function martingale is established for the important conditionally additive case. This result unifies those obtained separately for different examples and provides the key to asymptotic normality results for the maximum likelihood estimate.
38 citations
TL;DR: Under regularity conditions, a finite dimensional filter system exists for a partially observable process if and only if the conditional distributions involved each form an exponential family of distributions, and the filter equation can be derived directly from the exponential representations of these families as mentioned in this paper.
Abstract: Under regularity conditions, a finite dimensional filter system exists for a partially observable process if and only if the conditional distributions involved each form an exponential family of distributions. The filter equation can be derived directly from the exponential representations of these families.
37 citations
33 citations
TL;DR: In this article, asymptotic expansions of the distribution of the kth-largest order statistic Zn-k+1:n for the sample size n are presented. But the results are restricted to the case where the normal distribution is the leading term.
Abstract: This paper deals with asymptotic expansions of the distribution of the kth-largest order statistic Zn-k+1:n for the sample size n. These expansions establish higher-order approximations which hold uniformly over all Borel sets. In the particular case of the distribution of Zn-k+1:n under the uniform distribution and the exponential distribution, the approximating measures are linear combinations of 'negative' gamma distributions and linear combinations of extreme-value distributions. These results can be extended to the case of the joint distribution of the k largest order statistics. A numerical comparison to a different asymptotic expansion is given where the normal distribution is the leading term.
24 citations
21 citations
TL;DR: An easily implemented and computationally efficient procedure is presented for the generation of autocorrelated pseudo-random numbers with specific probability distributions.
Abstract: An easily implemented and computationally efficient procedure is presented for the generation of autocorrelated pseudo-random numbers with specific probability distributions. A plot illustrates the relationship among the autocorrelations of the uniform, Rayleigh, and exponential distributions corresponding to a given autocorrelation in the normal generating distribution.
TL;DR: In this article, the moments of the transformed family of distributions are calculated and the fitting of data to this family is illustrated with a numerical example and the resulting fit is compared with the Johnson's SB distribution fit.
Abstract: The distribution of y=e -1where I is distributed as a gamma random variable is considered(Grassia. 1977). It is shown that this transformed Family of distributions covers a wide region in the (√β1,β2) plane. The moments of this Family of distributions are easily calculated. The fitting of data to this family of distributions is illustrated with a numerical example and the resulting fit is compared with the Johnson's SB distribution fit.
TL;DR: Asymptotically best linear unbiased estimators (ABLUE) of quantiles, x^., in the two-parameter (location-scale) exponential and double exponential families are obtained as linear combinations of two suitably chosen order statistics as discussed by the authors.
Abstract: Asymptotically best linear unbiased estimators (ABLUE) of quantiles, x^., in the two-parameter (location-scale) exponential and double exponential families are obtained as linear combinations of two suitably chosen order statistics. Exact formulae for the linear combinations are given as functions of £. The derived estimators in both cases compare favorably with the usual nonparametric estimator. Also, in the exponential case the derived estimator compares favorably with the Sarhan-Greenberg BLUE based on a complete sample
TL;DR: In this paper, it was shown that if the distribution of min {X1/a1, X2/a2, XN/aN} is close to that of X1, then the distribution is very close to the exponential distribution.
Abstract: It is shown that if the distribution of min {X
1/a1, X2/a2,…, XN/aN} is close to that ofX
1, then the distribution is close to the exponential distribution.
TL;DR: In this article, a characterisation of the exponential distribution is discussed based on yet another extension of the lack of memory property, motivated by a functional equation appearing in Ahsannulah.
Abstract: In this note a charactrization of the exponential distribution is discussed based on yet another extension of the lack of memory property. The result was motivated by a functional equation appearing in Ahsannulah [1], [3]
TL;DR: In this article, the time evolution of a nonlinearly coupled system of first-order equations representing the Euler equations was studied and the probability distribution of functions is nearly Gaussian, while that of their time derivatives has exponential tails and moments of order 4, 6, and 8 that approach those of the exponential distributions.
Abstract: The statistics of the time evolution of a nonlinearly coupled system of first‐order equations representing the Euler equations is studied. The probability distribution of functions is nearly Gaussian, while that of their time derivatives has exponential tails and moments of order 4, 6, and 8 that approach those of the exponential distributions.
TL;DR: In this paper, it was shown that one may find a two-port subnetwork of the exponential distributed parameter (DP) Z-Y-KZ micro-circuit whose opencircuit voltage and shortcircuit current ratio-transfer functions are exactly the same as those of another two port subnetwork.
01 Jan 1981
TL;DR: In this paper, Srivastava's characterisation of the Exponential Distribution based on record values is presented, as well as the relationship between the conditional and unconditional distribution of a random variable.
Abstract: Section I: Continuous Models.- Statistical Predictive Distributions.- Hyperbolic Distributions and Ramifications: Contributions to Theory and Application.- Multivariate Distributions of Hyperbolic Type.- The Multimodal Exponential Families of Statistical Catastrophe Theory.- Regression Models for the Inverse Gaussian Distribution.- A Note on the Inverse Gaussian Distribution.- Some Properties of the Log-Laplace Distribution.- Compound Distributions Relevant to Life Testing.- Distributions Associated with Neutrality Properties for Random Proportions.- The Independence of Size and Shape Before and After Scale Change.- Distributions on the Simplex for the Analysis of Neutrality.- Section II: Discrete Models.- Chance Mechanisms for the Univariate Generalized Waring Distribution and Related Characterizations.- On a New Family of Discrete Distributions.- On the Stirling Distribution of the First Kind.- On the Moments and Factorial Moments of a MPSD.- On Bivariate Discrete Distributions Generated By Compounding.- Bivariate Generalized Discrete Distributions and Bipartitional Polynomials.- A Bivariate Hyper-Poisson Distribution.- On the Multinomial Distributions Generated By Stochastic Matrices and Applications.- Section III: Structural Properties.- Distributions with Sufficient Statistics for Multivariate Location Parameter and Transformation Parameter.- Analytic Distribution Functions.- Some Recent Statistical Results for Infinitely Divisible Distributions.- An Alternate Simpler Method of Evaluating the Multivariate Beta Function and an Inverse Laplace Transform Connected with Wishart Distribution.- On a Theorem of Polya.- Asymptotic Distributions of Functions of Eigenvalues.- Section IV: Computer Generation.- A Rejection Technique for the Generation of Random Variables with the Beta Distribution.- Fast Methods for Generating Bivariate Discrete Random Variables.- Frugal Methods of Generating Bivariate Discrete Random Variables.- Section V: Characterizations.- A Characterization of the Negative Multinomial Distribution.- On the Rao-Rubin Characterization of the Poisson Distribution.- On Some Characterizations of the Geometric Distribution.- On Splitting Model and Related Characterizations of Some Statistical Distributions.- Rao-Rubin Condition for a Certain Class of Continuous Damage Models.- On Matrix-Variate Beta Type I Distribution and Related Characterization of Wishart Distribution.- On the Relationship Between the Conditional and Unconditional Distribution of a Random Variable.- Some Bivariate Distributions of (X,Y) Where the Conditional Distribution of Y, Given X, is Either Beta or Unit-Gamma.- Some Relationships Between the Logistic and the Exponential Distributions.- Some Characterizations of the Exponential Distribution Based on Record Values.- A Note on Srivastava's Characterization of the Exponential Distribution Based on Record Values.- On the Stochastic Equation X+Y=XY.- On the Stability of Characterizations of Non-Normal Stable Distributions.- Author Index.
01 Jan 1981
TL;DR: In this article, a new family of discrete distributions is proposed, named simple meta-Poisson, whose unique parameter is the quadratic mean, and the potential usefulness of this distribution is confirmed by its fit compared with the fits of various two-parameters distributions.
Abstract: Starting from the expected value of a certain transformation of the Poisson random variable, a new family of discrete distributions is proposed. Special attention is given to particular members of the family. In this way a discrete distribution is obtained, named “simple meta-Poisson,” whose unique parameter is the quadratic mean. The potential usefulness of the simple meta-Poisson distribution is confirmed by its fit compared with the fits of various two-parameters distributions.
TL;DR: In this article, the problem of characterizing an exponential family by sufficiency of certain statistics is considered, and the authors do not want to characterize an expone family by a specific set of statistics.
Abstract: The problem of characterizing an exponential family by sufficiency of certain statistics is considered. In distinction to most of the papers on this subject we do not want to characterize an expone...
TL;DR: In this article, the uniformly most powerful unbiased tests for two sample problem of a given continuous distribution belonging to the exponential family with unknown scale and truncation parameters are formulated for two-parameter exponential and Paretc distributions.
Abstract: The uniformly most powerful unbiased tests are formulated for two sample problem of a given continuous distribution belonging to the exponential family with unknown scale and truncation parameters. The two-parameter exponential and Paretc distributions are considered in examples.