New estimators for the parameters of the Gamma distribution are proposed, which are used for constructing a test of fit for this model based on the ratio of two variance estimators. The asymptotic null distribution of the test statistic is also included.

This paper proposes a bootstrap goodness of fit test for the Generalized Pareto distribution (GPd) with shape parameter [gamma]. The proposed test is an intersection-union test which tests separately the cases of [gamma]=0 and [gamma]0 and rejects if both cases are rejected. If the test does not...

In this work we consider a power series of the form X=∑j=0∞δjZj where 0δ1 and {Zj}j≥0 is an i.i.d. sequence of random variables. We show that X is well-defined iff E[(log|Z0|)+]∞ and establish a number of properties of the distribution of X, such as continuity and closure under...

What is the distribution of the product of given powers of independent uniform (0, 1) random variables? Is this distribution useful? Is this distribution commonly used in some contexts? Is this distribution somehow related to the distribution of the product of other random variables? Are there...

If X1 and X2 are independent and identically distributed (i. i. d.) with finite variance, then (X1+X2)/[radical sign]2 has the same distribution as X1 if and only if X1 is normal with mean zero (Pólya [9]). The idea of using linear combinations of i. i. d. random variables to characterize the...