Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional Kolmogorov–Feller equations for the probabilities at...

Methods of Hilbert space theory together with the theory of analytic semigroups lead to an alternative approach for discussing an analytic birth and death process with the backward equations gk = [lambda]k - 1gk - 1 - ([mu]k+[lambda]k)gk+[mu]k+1, k = 0, 1, 2, ..., where [lambda]- 1 = 0 = [mu]0....

For a sample X1,X2,…XNof independent identically distributed copies of a log-logistically distributed random variable X the maximum likelihood estimation is analysed in detail if a left-truncation point xL0is introduced. Due to scaling properties it is sufficient to investigate the case xL=1....