No abstract

Point estimation of distribution parameters is considered for a three-parameter compound Poisson process. Formulas are derived for moment method estimation, including estimate biases and the covariance matrix. Asymptotic efficiency of the parameter estimates with a series informant is examined. The efficiency of moment method estimation is computed and analyzed for typical parameter values.

No abstract

No abstract

519.233.24 For the compound Poisson law generalized by the negative binomial distribution we derive the explicit representation of the probability function, the finite-difference recurrence, and expressions for the derivatives with respect to all parameters. Explicit representations of ordinary and factorial cumulants to sixth order are given and asymptotic normality of the distribution is proved. The distribution functions are constructed and analyzed for the most typical parameter values. Used to solve direct and inverse problems by moment methods.