A Bivariate Distribution Family with Specified Correlation Coefficient and Given Marginals

For given continuous distribution functions F(x) and G(y) and a Pearson correlation coefficient ρ, an algorithm is provided to construct a sequence of continuous bivariate distributions with marginals equal to F(x) and G(y) and the corresponding correlation coefficient converges to ρ. The algorithm can be easily implemented using S-Plus or R. Applications are given to generate bivariate random variables with marginals including Gamma, Beta, Weibull, and uniform distributions.     

On Block Skip Free Transition Matrices and First Passage Times

Starting from an abstract setting which extends the property “skip free to the left” for transition matrices to a partition of the state space, we develop bounds for the mean hitting time of a Markov chain to an arbitrary subset from an arbitrary initial law. We apply our theory to the embedded Markov chains associated with the M/G/1 and the GI/M/1 queueing systems. We also illustrate its applicability with an asymptotic analysis of a non-reversible Markovian star queueing network with losses.     

Modelling change in cognitive understanding with finite mixtures

Psychological theories often posit the existence of several different states. Individuals are viewed as belonging to one of the states at a given age, but with development pass to another state. A main problem in evaluating such theories is representing the transition from one state to another over age. A stochastic transition framework is proposed which should be useful in many different settings. The model is illustrated with data from a cognitive development task.     

A Characterization of the Normal Family of Distributions Based on the Bias of the Maximum Likelihood Estimator

This paper characterizes the family of Normal distributions within the class of exponential families of distributions, via the structure of the bias of the maximum likelihood estimator Θ _n of the canonical parameter Θ . More specifically, when E _θ ( Θ n ) – Θ = (1/ n ) Q ( Θ ) + o (1/ n ), the equality Q ( Θ ) = 0 proves to be a property of the Normal distribution only. The same conclusion is obtained for the one-dimensional case bt assuming that Q ( Θ ) is a polynomial of Θ .     

Bathtub distributions: a review

Bathtub distributions are characterized by bathtub failure rate functions . These are possibly more realisitic models than the monotone failure rate models . A systematic account of such distributions is not available and this review aims to give such an account . We give some easily verifiable conditions to check the bathtub property of a distribution along with methods to construct such distributions . We also discuss some stochastic and reliablity mechanisms which lead to bathtub distributions. These include mixtures ( stochastic failure rate models ) , series system , stochastic differential equation models and so on. We also review inference on bathtub distributions. The paper concludes with a rather exhaustive list of bathtub distributions.     

Bayesian analysis of threshold autoregressions

A nonasymptotic Bayesian approach is developed for analysis of data from threshold autoregressive processes with two regimes. Using the conditional likelihood function, the marginal posterior distribution for each of the parameters is derived along with posterior means and variances. A test for linear functions of the autoregressive coefficients is presented. The approach presented uses a posterior p-value averaged over the values of the threshold. The one-step ahead predictive distribution is derived along with the predictive mean and variance. In addition, equivalent results are derived conditional upon a value of the threshold. A numerical example is presented to illustrate the approach.     

Generalized polya eggenberger family of distributions and its relation to lagrangian katz family

Janardan (1973) introduced the generalized Polya Eggenberger family of distributions (GPED) as a limiting distribution of the generalized Markov-Polya distribution (GMPD). Janardan and Rao (1982) gave a number of characterizing properties of the generalized Markov-Polya and generalized Polya Eggenberger distributions. Here, the GPED family characterized by four parameters, is formally defined and studied. The probability generating function, its moments, and certain recurrence relations with the moments are provided. The Lagrangian Katz family of distributions (Consul and Famoye (1996)) is shown to be a sub-class of the family of GPED (or GPED ₁ ) as it is called in this paper). A generalized Polya Eggenberger distribution of the second kind (GPED ₂ ) is also introduced and some of it's properties are given. Recurrence relations for the probabilities of GPED ₁ and GPED ₂ are given. A number of other structural and characteristic properties of the GPED ₁ are provided, from which the properties of Lagrangian Katz family follow. The parameters of GMPD ₁ are estimated by the method of moments and the maximum likelihood method. An application is provided.     

Robust methods of estimation of regression coefficients 1

Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon's entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi's entropy, and study its properties. We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models.     

Comment

Bonferroni inequalities often provide tight upper and lower bounds for the probability of a union of events. The bounds are especially useful when this probability is difficult to compute exactly. There are situations, however, in which the Bonferroni approach gives very poor results. An example is given in which the upper and lower Bonferroni bounds are far from the probability they seek to approximate and successive bounds do not converge. Even an improved first upper Bonferroni bound may not be close to the probability of the union of events.     

Estimation of parameters of mixed failure time distribution

The problem of estimation of parameters of a mixture of degenerate and exponential distributions is considered. A new sampling scheme is proposed and the exact bias and the mean square error (MSE) of the maximum likelihood estimators of the parameters is derived. Moment estimators, their approximate biases and the MSE are obtained. Asymptotic distributions of the estimators are also obtained for both the cases.