A frequency-factor based approach for stochastic simulation of bivariate gamma distribution is proposed. The approach involves generation of bivariate normal samples with a correlation coefficient consistent with the correlation coefficient of the corresponding bivariate gamma samples. Then the bivariate normal samples are transformed to bivariate gamma samples using the well-known general equa...

We provide a new characterization of the Bivariate normal-Wishart distribution. Let ~ x = fx 1 ; x 2 g have a non-singular Bivariate normal pdf f(~ x) = N(~ ; W) with unknown mean vector ~ and unknown precision matrix W. Let f(~ x) = f(x 1)f(x 2 jx 1) where f(x 1) =

Let X1 and X2 be two identically distributed random variables. Suppose that X1 | X2=x2 has a N(ax2+b, _) distribution for all x2 # R, where & 0. Ahsanullah (1985) showed that these conditions imply |a|<1, X1 , and X2 have a common normal distribution with mean b (1&a;) and variance _ (1&a;), and the joint distribution of X1 and X2 is a bivariate normal distribution with covariance a_ (...

To model correlated bivariate count data with extra zero observations, this paper proposes two new bivariate zero-inflated generalized Poisson (ZIGP) distributions by incorporating a multiplicative factor (or dependency parameter) λ, named as Type I and Type II bivariate ZIGPλ distributions, respectively. The proposed distributions possess a flexible correlation structure and can be used to fit...

Multivariate statistical process control deserves particular attention in the recent scenario. Though, Hotelling control chart is quite popular and widely used technique in this field but its performance is deteriorated when the underlying distribution of the quality characteristics is not following multivariate normal distribution. Hence the need of developing a non-parametric multivariate con...

In a bivariate data plot, every two points determine an “elementary slope.” For n points with distinct x-values, there are n(n – 1)/2 elementary slopes. These elementary slopes are examined under the two classical regression assumptions: (1) the regressor variable values are fixed and the error is independent and normal, and (2) the data is bivariate normal. For case (1), it is demonstrated tha...