Topic
Natural exponential family
About: Natural exponential family is a research topic. Over the lifetime, 1973 publications have been published within this topic receiving 60189 citations. The topic is also known as: NEF.
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TL;DR: In this paper, a new lifetime distribution which accommodates decreasing and unimodal hazard function is proposed, which is derived from the exponentiated complementary exponential geometric distribution and has it genesis on the compounding the exponential and geometric distributions.
Abstract: A new lifetime distribution which accommodates decreasing and unimodal hazard function is proposed in this paper. It is derived from the exponentiated complementary exponential geometric distribution and has it genesis on the compounding the exponential and geometric distributions. It can be used on a latent complementary causes scenario, where onle thethe minimum lifetime among all causes is observed. We derive the density, quantile, survival and failure rate functions for the proposed distribution, as well as some proprieties such as the characteristic function, mean, variance and r-th order statistics. The estimation is based on maximum likelihood approach. A simulation study performed in order to assess the performance of the maximum likelihood estimates of the parameters of the proposed distribution. The methodology is illustrated in three real datasets.
3 citations
TL;DR: The α-power transformation (APT) family of distributions proposed in this journal by Mahdavi and Kundu (2017) is not new, but the same as theexp-G family of distribution as discussed by the authors.
Abstract: Dear Editor,The “α-power transformation” (APT) family of distributions recently proposed in this journal by Mahdavi and Kundu (2017) is not new, but the same as the “exp-G” family of distributions ...
3 citations
TL;DR: In this article, bounds on the uniform distance between a χ22n distribution and the distribution of 2Σni = 1 Xi/μ, where X1, X2, Xn are n independent, identically distributed nonnegative random variables with common mean μ, are derived assuming that the Xi's are HNBUE or HNWUE or that a specific "mechanism" is "perturbing" an exponential distribution.
3 citations
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TL;DR: In this article, it was shown that a generalized gamma distribution with shape and exponent power parameters no greater than one is a mixed exponential distribution, and that the mixing distribution is written out explicitly as a scale mixture of strictly stable laws concentrated on the nonnegative halfline.
Abstract: A new class of discrete GG-mixed Poisson distributions is considered as the family of mixed Poisson distributions in which the mixing laws belong to the class of generalized gamma (GG) distributions. The latter was introduced by E. W. Stacy as a special family of lifetime distributions containing gamma, exponential power and Weibull distributions. It is proved that a generalized gamma distribution with shape and exponent power parameters no greater than one is a mixed exponential distribution. The mixing distribution is written out explicitly as a scale mixture of strictly stable laws concentrated on the nonnegative halfline. As a corollary, the representation is obtained for the GG-mixed Poisson distribution as a mixed geometric distribution. The corresponding scheme of Bernoulli trials with random probability of success is considered. Within this scheme, a random analog of the Poisson theorem is proved establishing the convergence of mixed binomial distributions to mixed Poisson laws. Limit theorems are proved for random sums of independent random variables in which the number of summands has the GG-mixed Poisson distribution and the summands have both light- and heavy-tailed distributions. Various representations for the limit laws are obtained in terms of mixtures of Mittag-Leffler, Linnik or Laplace distributions. Limit theorems are proved establishing the convergence of the distributions of statistics constructed from samples with random sizes obeying the GG-mixed Poisson distribution to special normal mixtures.
3 citations
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.
3 citations