English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Abstract We shall derive the moment of the ratio Y=(X + Y ) and the reliability P(X < Y ),and then observe the skewness of the ratio in a bivariate Pareto density function of(X;Y ). And we shall consider an approximate MLE of parameters in the bivariatePareto density function.Keywords: Approximate maximum likelihood estimation, bivariate Pareto distribution,generalized hypergeometric function, reliability, skewness. 1. Introduction Many authors have studied estimations and characterizations in a bivariate Pareto distri-bution with three parameters , and ˙, whose distribution was used widely in economicapplications in Johnson et al. (1994).For two random variables Xand Y, and a real number c, the probability P(X<cY) is adistribution function of the ratio Y=(X+ Y) when c= t=(1 t) for 0 <t<1.For given random variables Xand Y, the distribution of the ratio R= Y=(X+ Y) is ofinterest in biological and physical sciences, econometrics, engineering. For example, ratios ofnormal variables appear as sampling distributions of single equation models in simultaneousequations models. Other area of applications includes the mass to energy ratios in nuclearphysics.The problem of estimating the probability that a random variable Xis less than anotherrandom variable Y arises in many practical situations, like economics study. The problemhas been studied by many authors for di erent distributions of Xand Y; see, for example Palet al. (2005), Raqab et al. (2007) and Ali et al. (2010). Woo (2007) also studied the reliabilityin two independent half-triangle distributions. Moon and Lee (2009) studied an inference onthe reliability P(Y <X) in the Gamma case. Moon et al. (2009) studied inferences for thereliability and the ratio in an exponentiated complementary power function distribution.

Moment of the ratio and approximate MLEs of parameters in a bivariate Pareto distribution