The Bivariate Normal Probability Distribution

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...

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 ...

Bivariate Joint Probability Distribution for Correlated M-Distributed Variables

10GHz 以上の無線回線設計においては,降雨によ る減衰が大きな問題となる.このため信頼性の高い無 線回線を経済的に設計するためには,回線設置地域に おける降雨減衰確率を統計的に精度良く推定する必要 があり,降雨強度や降雨減衰の確率分布をモデル化し た種々の推定法が提案されている.このような降雨強 度及び降雨減衰の確率分布として,従来,時間率の大 きな領域では対数正規分布が,時間率の小さい領域で はガンマ分布が良い近似を与えるモデルとして広く用 いられてきたが,更に,通信回線の設計で問題となる 強降雨強度・短時間率領域を含めて広い累積時間領域 にわたって降雨強度の統計累積分布をよく近似する分 布としてMoupfouma分布 [1], [2]が知られている.し かしながら,Moupfouma分布は分布の平均値や分散 と分布パラメータの関係を容易に計算できないことな どから,降雨減衰推...

A Characterization of the Bivariate Normal-Wishart Distribution

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. L e t f(~ x) = f(x 1)f(x 2 jx 1) where f(x 1) = N(m 1 1=v 1) and f(x 2 jx 1) = N(m 2j1 +b 12 x 1 1=v 2j1). Similarly, deene fv 2 v 1j2 b 21 m 2 m 1j2 g using the factorization f(~ ...

Estimation Using Bivariate Extreme Ranked Set Sampling With Application To The Bivariate Normal Distribution