En este trabajo se proponen dos posibles estimadores del parámetro de dependencia de una familia de distribuciones bivariantes con marginales dadas y se realiza un estudio de Monte Carlo de sus respectivos sesgo y eficiencia, a fin de determinar cuál de ambos estimadores es preferible. También se propone y se estudia, de forma similar, una posible versión "Jackknife" del mejor de los dos estimadores anteriores. En este estudio se emplean técnicas de reducción de la varianza. Para poder realizar...

Generalized length biased distribution is defined as $h\left(x\right)={\phi }_r\left(x\right)f\left(x\right),x>0$, where $f\left(x\right)$ is a probability density function, ${\phi }_r\left(x\right)$ is a polynomial of degree $r$, that is, ${\phi }_r\left(x\right)=a_1(x/{\mu }_1^{\text{'}})+...+a_r(x^r/{\mu }_r^{\text{'}})$, with $a_i>0,i=1,...,r,a_1+...+a_r=1,{\mu }_i^{\text{'}}=E\left(x^i\right)$ for $f\left(x\right),i=1,2...,r$. If $r=1$, we have the simple length biased distribution of Gupta and Keating [1]. First, characterizations of exponential, uniform and beta distributions are given in terms of simple length biased distributions. Next, for the case of generalized distribution, the distribution of the sum of $n$ independent variables is put in the closed form when $f\left(x\right)$...

The concepts of geometric infinite divisibility and stability extend the classical properties of infinite divisibility and stability to geometric convolutions. In this setting, a random variable X is geometrically infinitely divisible if it can be expressed as a random sum of $N_p$ components for each p ∈ (0,1), where $N_p$ is a geometric random variable with mean 1/p, independent of the components. If the components have the same distribution as that of a rescaled X, then X is (strictly) geometric stable....

The aim of the paper is to present a test of goodness of fit with weigths in the classes based on weighted $\left(h,\phi \right)$-divergences. This family of divergences generalizes in some sense the previous weighted divergences studied by Frank et al [frank] and Kapur [kapur]. The weighted $\left(h,\phi \right)$-divergence between an empirical distribution and a fixed distribution is here investigated for large simple random samples, and the asymptotic distributions are shown to be either normal or equal to the distribution of a linear...

Using characterization conditions of continuous distributions in terms of moments of order statistics given in [12], [23], [6] and [7] we present new goodness-of-fit techniques.

Using characterization conditions of continuous distributions in terms of moments of order statistics and moments of record values we present new goodness-of-fit techniques.