Conditions for bimodality of mixtures of two unimodal distributions are investigated in some special cases. Based on general characterizations, explicit criteria for the parameters are derived for mixtures of two Cauchy, logistic, Student, gamma, log-normal, Gumbel and other distributions.

The family of proper conjugate priors is characterized in a general exponential model for stochastic processes which may start from a random state and/or time.

Let (X1,Y1),...,(Xm,Ym) be m independent identically distributed bivariate vectors and L1 = β1X1 + ... + βmXm, L2 = β1X1 + ... + βmXm are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of L1 and L2 imply the same property for X1 and Y1, and under what conditions does the independence of L1 and L2 entail independence of X1 and Y1? Some analytical sufficient conditions are obtained and it is shown that in general they can not be...

Let $(X_1,Y_1),...,(X_m,Y_m)$ be $m$ independent identically distributed bivariate vectors and $L_1={\beta }_1{X}_1+...+{\beta }_m{X}_m$, $L_2={\beta }_1{Y}_1+...+{\beta }_m{Y}_m$ are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of $L_1$ and $L_2$ imply the same property for $X_1$ and $Y_1$, and under what conditions does the independence of $L_1$ and $L_2$ entail independence of $X_1$ and $Y_1$? Some analytical sufficient conditions are obtained and it is shown that in general they can not be weakened.

On bounded or unbounded intervals of the real line, we introduce classes of regular statistical families, called Johnson families because they are obtained using generalized Johnson transforms. We study in a rigorous manner the formerly introduced concept of core function of a distribution from a Johnson family, which is a modification of the well known score function and which in a one-to-one manner represents the distribution. Further, we study Johnson parametrized families obtained by Johnson...