Bayesian estimation of incomplete data using conditionally specified priors

In this paper, a class of conjugate prior for estimating incomplete count data based on a broad class of conjugate prior distributions is presented. The new class of prior distributions arises from a conditional perspective, making use of the conditional specification methodology and can be considered as the generalisation of the form of prior distributions that have been used previously in the estimation of in- complete count data well. Finally, some examples of simulated and real data are given

A generalization of the credibility theory obtained by using the weighted balanced loss function

In this paper an alternative to the usual credibility premium that arises for weighted balanced loss function is considered. This is a generalized loss function which includes as a particular case the weighted quadratic loss function traditionally used in actuarial science. From this function credibility premiums under appropriate likelihood and priors can be derived. By using weighted balanced loss function we obtain, first, generalized credibility premiums that contain as particular cases other credibility premiums in the literature and second, a generalization of the well-known distribution free approach in [Bühlmann, H., 1967. Experience rating and credibility. Astin Bull. 4 (3), 199-207].

The Slashed-Rayleigh Fading Channel Distribution

We propose an alternative distribution for modelling fading-shadowing wireless channels. This distribution presents certain advantages over the Rayleigh-lognormal distribution and the K distribution and has proved useful in the setting described. We obtain closed-form expressions for the average channel capacity and for the average bit error rate of differential phase-shift keying and of minimum shift keying when the new distribution is used. This distribution can be obtained exactly as the sum of mutual independent Gaussian stochastic processes, because it must represent the simulation of the fading channel; that is, it simulates the signal envelope. Finally, we describe practical applications of this distribution, comparing it with the Rayleigh-lognormal and K distributions

On the Usefulness of the Logarithmic Skew Normal Distribution for Describing Claims Size Data

In this paper, the three-parameter skew lognormal distribution is proposed to model actuarial data concerning losses. This distribution yields a satisfactory fit to empirical data in the whole range of the empirical distribution as compared to other distributions used in the actuarial statistics literature. To the best of our knowledge, this distribution has not been used in insurance context and it might be suitable for computing reinsurance premiums in situations where the right tail of the empirical distribution plays an important role. Furthermore, a regression model can be simply derived to explain the response variable as a function of a set of explanatory variables

The Poisson-conjugate Lindley mixture distribution

A new discrete distribution that depends on two parameters is introduced in this article. From this new distribution the geometric distribution is obtained as a special case. After analyzing some of its properties such as moments and unimodality, recurrences for the probability mass function and differential equations for its probability generating function are derived. In addition to this, parameters are estimated by maximum likelihood estimation numerically maximizing the log-likelihood function. Expected frequencies are calculated for different sets of data to prove the versatility of this discrete model