The ageing curve and partial orderings of life distributions

In this paper we define a new measure to describe the process of ageing of lifetime distributions. In terms of this measure we will define three partial orderings of lifetime distributions. The relationships between these orderings and other classical orderings are studied.     

A general family of NBU classes of life distributions

In this paper we introduce and study a family of new better than used ageing notions parameterized by a function h. The new better than used , the new better than used of a specified age and the new better than used in total time on test transform order , are special cases of this new family. We study some properties of the new family, and we give some applications of it in actuarial science, reliability theory and statistics.     

Preservation of generalized ageing classes on the residual life at random time

In this paper, we provide some new preservation properties of generalized ageing classes (s-IFR) on the residual life at random time, where s is a nonnegative integer. We also obtain bounds of the residual life at exponential random time. Results are expected to be useful in the reliability, queue theory and actuarial science.     

New classes of discrete bivariate distributions with application to football data

Motivated by Lee and Cha [The American Statistician 69 (2015) 221–230], we introduce 18 new families of discrete bivariate distributions. We give explicit expressions for their probability mass functions, cumulative distribution functions, product moments, and moment-generating functions. We reanalyze the football data in Lee and Cha (2015 Lee, H., Cha, J.H. (2015). On two general classes of discrete bivariate distributions. Am. Stat. 69:221–230.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and show that some of the newly proposed distributions provide better fits than the two families proposed by Lee and Cha.     

On some models leading to the generalized poisson distribution

A new generalization of the Poisson distribution was given by Consul and Jain (1970, 73). Since then more than twenty papers, written by various researchers, have appeared on this model under the titles of Generalized Poisson Distribution (GPD), Lagrangian Poisson distribution or modified power series distribution. Here the author provides two physical models, based on differential-difference equations, which lead to the GPD. A number of axioms are given for a steady state point process which produce the generalized Poisson process. Also, the GPD is derived as the limiting distribution of the two quasi-binomial distributions based on urn models.     

Some classes of four-weight spin models

We classify four-weight spin models (X;W₁,W₂,W₃,W₄) with sizes at most four. We also study the class of four-weight spin models with exactly two distinct values in W₄, reduce their existence to that of certain symmetric designs.     

Some classes of distributions and their application in queueing

New classes of distributions are defined in analogy to the properties NBU, NBUE known from reliability. They are applied to obtain bounds on certain parameters of the GI/G/1 queue, such as the mean and the variance of the stationary waiting time, the probability of waiting, and the covariances of waiting times.     

A note on rescalings,reparametrizations and classes of distributions

Families of distributions on the real line have location, scale and shape parameters. Reparametrizations of such distributions, particularly involving rescalings, do not produce different families of distributions. However, from time to time, ‘extended’ or ‘generalized’ distributions are proposed that are nothing other than such reparametrizations. This note was triggered by a specific instance recently published in this journal but other examples are briefly mentioned as well.     

Characterization of distributions in invariant models

The theorem of Kagan et al. (1967), (Sankhya Ser. A. 27, 405) on the characterization of the normal law is extended to the characterization of a broad class of distribution shapes, also in the linear regression model, and the stability of this characterization is considered. The results enable, among others, to construct an asymptotically efficient estimator from a subclass of equivariant asymptotically linear estimators of θ.     

On characterizing mixtures of some life distributions

Received: October 15, 1998; revised version: January 10, 2000     

The impact of fat-tailed distributions on some leading unit roots tests

There is substantial evidence that many time series associated with financial and insurance claim data are fat-tailed, with a (much) higher probability of " outliers' compared with the normal distribution. However, standard tests, or variants of them, for the presence of unit roots assume a normal distribution for the innovations driving the series. Application of the former to the latter therefore involves an inconsistency. We assess the impact of this inconsistency and provide information on its impact on inference when innovations are drawn from the Cauchy and sequence of t(v) distributions. A simple prediction that fat tails will uniformly lead to over-sizing of standard tests (because the fatness in the tail translates to the test distribution) turns out to be incorrect: we find that some tests are over-sized but some are under-sized. We also consider size retention and the power of the Dickey-Fuller pivotal and normalized bias test statistics and weighted symmetric versions of these tests. To make the unit root testing procedure feasible, we develop an entropy-based test for some fat-tailed distributions and apply it to share prices from the FTSE100.     

A new family of life distributions based on the elliptically contoured distributions

In this article we propose a new family of life distributions, generated from an elliptically contoured distribution, in which the density and some of its properties are obtained. Explicit expressions for the density are found for a large number of specific elliptical distributions, such as Pearson type VII, t, Cauchy, Kotz type, normal, Bessel, Laplace and logistic.     

Statistical inference for a class of life distributions

Life distributions with hazard rate functions of the form r(t) = Ag(t) + Bh(t) are considered. It is assumed that g(t) and h(t) are known and are independent of the unknown parameters A and B. The maximum likelihood estimators are studied for complete and censored samples. The estimation problem is reduced to a solution of one equation with one unknown parameter and it is observed that the solution is unique. The estimation procedure under the assumption of aging is also described. Some comments about the asymptotic variance-covariance matrix are given, and tests of hypo-theses are described for some cases.     

A new test to detect monotonic and non-monotonic types of heteroscedasticity

A direct parametric test is proposed to detect monotonic and non-monotonic types of heteroscedasticity. After giving brief information about non-monotonic types of heteroscedasticity, the test algorithm is introduced. Proposed test and usual heteroscedasticity tests are compared on monotonic and non-monotonic types of heteroscedasticity in real and artificial data.     

A new class of multivariate skew distributions with applications to bayesian regression models

Abstract: The authors develop a new class of distributions by introducing skewness in multivariate elliptically symmetric distributions. The class, which is obtained by using transformation and conditioning, contains many standard families including the multivariate skew‐normal and t distributions. The authors obtain analytical forms of the densities and study distributional properties. They give practical applications in Bayesian regression models and results on the existence of the posterior distributions and moments under improper priors for the regression coefficients. They illustrate their methods using practical examples.     

A new class of multivariate skew distributions with applications to Bayesian regression models

The original article to which this Erratum refers was published in The Canadian Journal of Statistics, Vol. 31, No. 2, 2003, pp. 129–150.     

An omnibus test of goodness-of-fit for conditional distributions with applications to regression models

We introduce an omnibus goodness-of-fit test for statistical models for the conditional distribution of a random variable. In particular, this test is useful for assessing whether a regression model fits a data set on all its assumptions. The test is based on a generalization of the Cramér–von Mises statistic and involves a local polynomial estimator of the conditional distribution function. First, the uniform almost sure consistency of this estimator is established. Then, the asymptotic distribution of the test statistic is derived under the null hypothesis and under contiguous alternatives. The extension to the case where unknown parameters appear in the model is developed. A simulation study shows that the test has good power against some common departures encountered in regression models. Moreover, its power is comparable to that of other nonparametric tests designed to examine only specific departures.