Distribution of linear combination of exponential variates

The exact distribution of a linear combination of n independent negative exponential random variables, when the coefficients of the linear combination are distinct and positive quantities, is well-known. This paper extends the above result to the general case, namely when the coefficients are arbitrary real numbers, positive or negative, distinct or coincident.     

Gramatica de la Mente y Conocimiento Tacito

Resumen

Este artículo se ha centrado en las limitaciones que han encontrado los intentos de construir modelos formales del conocimiento humano y en el significado de dichas limitaciones. Se ha argumentado que dichas limitaciones tienen su origen en el hecho de que las reglas que constituyen la gramática de la mente son reglas sensibles a los contextos, en oposición a puramente formales.

Todo ello nos ha llevado ha exponer la tesis de que en el mundo social el conocimiento existe encarnado en individuos, pero no puede ser explicado desde el individuo, requiere un marco social. Y si esto es así, la Psicología cognitiva debe ser reinterpretada como psicología social del conocimiento.

Nuestra apuesta personal es que el desarrollo futuro de esta posición será tanto más prometedor cuanto más uso sepa hacer de lo que ya empieza a ser llamado “Epistemología de la complejidad” (véase Jantsch, 1981; Guidano, en prensa; Ibáñez, 1986; Miró en prensa, b). El desarrollo de este reto, sin embargo, pertenece todavía al futuro de la investigación.     

Characterizations of geometric distribution and discrete IFR (DFR) distributions using order statistics

Let X be a discrete random variable the set of possible values (finite or infinite) of which can be arranged as an increasing sequence of real numbers a₁<a₂<a₃<…. In particular, a_i could be equal to i for all i. Let X_1n≦X_2n≦?≦X_nn denote the order statistics in a random sample of size n drawn from the distribution of X, where n is a fixed integer ≧2. Then, we show that for some arbitrary fixed k(2≦k≦n), independence of the event {X_kn=X_1n} and X_1n is equivalent to X being either degenerate or geometric. We also show that the montonicity in i of P{X_kn = X_1n | X_1n = a_i} is equivalent to X having the IFR (DFR) property. Let a_i = i and $\text{G(i) = P(X≧i), i = 1, 2, …}$. We prove that the independence of {X_2n ? X_1n ∈B} and X_1n for all i is equivalent to X being geometric, where B = {m} (B = {m,m+1,…}), provided G(i) = q^i?1, 1≦i≦m+2 (1≦i≦m+1), where 0<q<1.     

Estimation of the parameters of a regression model with a multivariate t error variable

This paper deals with a regression model for several vari¬ables under the assumption that the errors have a multivariate t-distribution. The parameters of the model, the regression parameters, as well as the scale parameters and the degress of freedom of the error variable are estimated and the estimation procedure is illustrated by a numerical example, Also, the prop¬erties of the estimators and tests for the regression parameters are discussed.     

The modified permutation entropy-based independence test of time series

Abstract

In time series, it is essential to check the independence of data by means of a proper method or an appropriate statistical test before any further analysis. Therefore, among different independence tests, a powerful and productive test has been introduced by Matilla-García and Marín via m-dimensional vectorial process, in which the value of the process at time t includes m-histories of the primary process. However, this method causes a dependency for the vectors even when the independence assumption of random variables is considered. Considering this dependency, a modified test is obtained in this article through presenting a new asymptotic distribution based on weighted chi-square random variables. Also, some other alterations to the test have been made via bootstrap method and by controlling the overlap. Compared with the primary test, it is obtained that not only the modified test is more accurate but also, it possesses higher power.     

Reliability estimation based on ranked set sampling

In this paper we consider the problem of estimating the reliability of an exponential component based on a Ranked Set Sample (RSS) of size n. Given the first r observations of that sample, 1≤r≤n, we construct an unbiased estimator for this reliability and we show that these n unbiased estimators are the only ones in a certain class of estimators. The variances of some of these estimators are compared. By viewing the observations of the RSS of size n as the lifetimes of n independent k-out-of-n systems, 1≤k≤n, we are able to utilize known properties of these systems in conjunction with the powerful tools of majorization and Schur functions to derive our results.     

The Attitude of the Shari'a Courts to Parental Alienation Syndrome: Understanding the Dynamics of the Syndrome in Arab Society

In addition to the many factors leading to parental alienation syndrome (PAS), including the narcissistic injury felt by the abandoned parent, or the custodial parent's personal difficulty, there are further factors unique to Arab society—including strong influence by the extended family on the child. Although all the components of PAS exist and are well known to the shari'a courts, no parallel concept is found in the Arab legal lexicon. This article presents 1 case of a shari'a court hearing that illustrates this phenomenon. The conclusions indicate that the shari'a court considers this a serious phenomenon and sees coping with the situation as an essential and preliminary condition to the custody hearing.     

Approximations of Variances and Covariances for Order Statistics from the Standard Extreme Value Distribution

We consider simple approximations of variances and covariances for order statistics from the standard extreme value distribution. Exact values and simulation results of the variances and covariances for certain sample sizes are used to determine the validity of the suggested approximations.