We investigate the possibility of approximating the variance gamma distribution with a finite mixture of normals. Therefore, we apply this result to derive a simple historical estimation procedure by means of the Expectation Maximization algorithm.

The Fisher information on θ of the r-size weighted pdf fr(x;θ) and its parent pdf f(x;θ) are compared leading to some characterization properties for f(x;θ). Additionally, some bounds for the Fisher information in terms of r are also presented.

The aim of this work is to provide some characterization properties of the log-normal distribution with the help of divergence measures between a probability density function f and its r-size weighted counterpart fr. The characterization can be expressed in terms the Kullback–Leibler, the...

We provide simple computational formulas of both expected termination time and Fisher information of the flexible progressive censoring scheme proposed by Bairamov and Parsi (2011). Then, the design and planning of the flexible progressive censoring schemes are discussed with illustrative examples.

The geometric process is considered when the distribution of the first interarrival time is assumed to be exponential. An analytical expression for the one dimensional probability distribution of this process is obtained as a solution to a system of recursive differential equations. A power...

Cumulative residual entropy has been proposed by Rao et al. (2004). In this paper, we first show a representation of the cumulative residual entropy of the first r order statistics as a single integral. Then we provide some related results including recurrence relations, identity and...

Beyond the expectation–maximization (EM) algorithm for vector parameters, the EM for an unknown distribution function is often used in mixture models, density estimation, and signal recovery problems. We prove the convergence of the EM in functional spaces and show the EM likelihoods in this...

The em algorithm can be used to compute maximum likelihood estimates of model parameters for skew-t mixture models. We show that the intractable expectations needed in the e-step can be written out analytically. These closed form expressions bypass the need for numerical estimation procedures,...

Nonlinear state space models with mixed-effect (NLMESSM) are proposed to model HIV clinical longitudinal data. With NLMESSM, filtering algorithms are proposed to estimate the individual/population states. Maximum likelihood via iterated filtering and variance components model are proposed to...