On Samples from a Normal Bivariate Population

Distribution of Quantiles in Samples from a Bivariate Population

Let F (x,y) be t he joint d istri but ion function of (X, y), possessing a probability density funct ion f(x,y). Let F I(X) and l>'2(Y) be the marginal distribut ion fun ctions of X and Y respectively. Let a be a quantile of FI (x) and f3 be a quantile of F2(y). A random sampl e (X k, Y k), k= 1, 2, ... , n, is drawn a nd t he values on each variate are ordered so that X:< X; a nd Y;< Y; if i <...

Asymptotic Efficiencies of the MLE Based on Bivariate Record Values from Bivariate Normal Distribution

Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is ...

The Bivariate Normal Distribution

Let U and V be two independent normal random variables, and consider two new random variables X and Y of the form X = aU + bV, Y = cU + dV, where a, b, c, d, are some scalars. Each one of the random variables X and Y is normal, since it is a linear function of independent normal random variables.† Furthermore, because X and Y are linear functions of the same two independent normal random variab...

A Characterization of the Bivariate Normal

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) =

The asymptotical distribution of range in samples from a normal population.