In this article a characterisation of the Gumbel's Bivariate Exponential Distribution is established on the basis of the propertiea of the conditional expectation of the component variables. The characterieing property is propoeed as the definition of lack of memory in the biveriate case.
A characterization of the wald distribution
โ Scribed by M. Ahsanullah; S. N. U. A. Kirmani
- Publisher
- John Wiley and Sons
- Year
- 1984
- Tongue
- English
- Weight
- 157 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0894-069X
No coin nor oath required. For personal study only.
โฆ Synopsis
Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F ( x ) has the Wald distribution. A relation between the probability density function of X-' with that of X is used to characterize the Wald distribution.
x > 0, A, p > 0, (3) in such situation. Here p. is the mean and h is a shape parameter. The inverse Gaussian
๐ SIMILAR VOLUMES
ther investigation of the characteristics of the apo(a) isoform-independent Lp(a) distribution is warranted. o 1995 Wiley-Liss, Inc.
Suppose X,, X,, ..., X, are independent and identically distributed random variables with absolutely continuous distribution function F. It is known that if F is standard normal distribution then (i) 2 X : is a chi-square with n degrees of freedom and (ii) nX2 is a chi-square with 1 degrees of freed
Denoting by \(X_{(1,} \leqslant X_{t 2} \leqslant \cdots \leqslant X_{(n)}\) the order statistic based on a random sample \(X_{1}, X_{2}, \ldots, X_{n}\) drawn from a distribution \(F\), it is shown that the property " \(E\left(X_{1} \mid X_{(1)}, X_{(n)}\right)=\frac{1}{2}\left(X_{(1)}+X_{(n)}\righ