On a preliminary test estimator for one of the parameters of the log-zero-poisson distribution

A discrete distribution called the log-zero-Poisson distribution has been recommended by Katti (c.f. Biometrics 1970) as an alternate to the negative binomial and other distributions usually called "contagious" distributions.A major problem in the use of this and all other contagious distributions has been the difficulty of obtaining the maximum likelihood esti-mates. A custom-made ad hoc estimator, λ, has been proposed for the parameter λ of this distribution in Katti and Khedr (1980). In this paper, its efficiency relative to Fisher information is studied, only to discover that λ can be 30 times better than the maximum likelihood estimate in some parts of the parameter space and much weaker in other parts.A preliminary test is recommended to choose between the estimates, and the efficiency of the procedure is tabulated. As it is to be expected, the resultant estimator equals the better of the two estimators with some error at the values of the parameters where the two estimators are equivalent.     

Optimal allocation of time points for the random effects model

In this article the problem of the optimal selection and allocation of time points in repeated measures experiments is considered. D‐ optimal designs for linear regression models with a random intercept and first order auto‐regressive serial correlations are computed numerically and compared with designs having equally spaced time points. When the order of the polynomial is known and the serial correlations are not too small, the comparison shows that for any fixed number of repeated measures, a design with equally spaced time points is almost as efficient as the D‐ optimal design. When, however, there is no prior knowledge about the order of the underlying polynomial, the best choice in terms of efficiency is a D‐ optimal design for the highest possible relevant order of the polynomial. A design with equally‐spaced time points is the second best choice     

Fisher Information Matrix for the Generalized Feller-Pareto Distribution

In this article, the exact form of Fisher information matrix for the generalized Feller-Pareto (GFP) distribution is determined. The GFP family is a general distribution which includes a variety of distributions as special cases. For example:

??generalized Singh-Maddala distribution which in turn includes Burr, Fisk, and Lomax distribution (see Kleiber and Kotz, 2003 Kleiber, C., Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences. Hoboken, NJ: John Wiley.[Crossref] , [Google Scholar]);

??a Pareto IV distribution which includes a hierarchy of Pareto models, omitted an additional location parameter (see Arnold, 1983 Arnold, B.C. (1983). Pareto Distributions. Fairland, MD: International Cooperative Publishing House. [Google Scholar], 2008 Arnold, B.C. (2008). Pareto and generalized pareto distributions. In: Modeling Income Distributions and Lorenz Curves, Economic Studies in Equality, Social Exclusion and Well-Being, Chotikapanich, D. (Ed.), New York: Springer. pp. 119–145.[Crossref] , [Google Scholar]); and

??beta Lomax distribution which includes, for example, beta II and Lomax distributions.

Application of these distributions covers a wide spectrum of areas ranging from actuarial science, economics, finance to bioscience, telecommunications, and medicine.     

Minimum and Maximum Information Censoring Plans in Progressive Censoring

Expressions for the entropy, the Kullback-Leibler information, and the I _α-information are established for distributions of progressively Type-II censored order statistics. These results are used to identify minimum and maximum information censoring plans. In particular, we find minimum and maximum entropy plans for DFR, exponential, Pareto, reflected power, and Weibull distributions. The results for Kullback-Leibler and I _α-information hold for any continuous distribution.     

Akaike Information Criterion for Selecting Variables in the Nested Error Regression Model

The Akaike Information Criterion (AIC) is developed for selecting the variables of the nested error regression model where an unobservable random effect is present. Using the idea of decomposing the likelihood into two parts of “within” and “between” analysis of variance, we derive the AIC when the number of groups is large and the ratio of the variances of the random effects and the random errors is an unknown parameter. The proposed AIC is compared, using simulation, with Mallows' C _p , Akaike's AIC, and Sugiura's exact AIC. Based on the rates of selecting the true model, it is shown that the proposed AIC performs better.     

Renyi Entropy Properties of Order Statistics

In this article, we discuss some properties of Renyi entropy and Renyi information of order statistics. Some bounds for Renyi entropy of order statistics are obtained. Also, we relate Renyi entropy ordering of order statistics to Renyi entropy ordering and other well known orderings of parent random variables. Then it is proved that the Renyi information between order statistics and parent random variable is distribution free, and it is shown, as expected, the distance is minimum for the median.     

Some inference results in several symmetric multivariate exponential models

In this paper, we consider multivariate exponential models with identical marginals. We obtain MLEs of the parameters and large sample tests for mutual independence of k components in the multivariate exponential models proposed by Weinman (1966), Marshall-Olkin (1967) and Block (1975).     

Shannon Information Properties of the Endpoints of Record Coverage

This paper addresses the largest and the smallest observations, at the times when a new record of either kind (upper or lower) occurs, which are it called the current upper and lower record, respectively. We examine the entropy properties of these statistics, especially the difference between entropy of upper and lower bounds of record coverage. The results are presented for some common parametric families of distributions. Several upper and lower bounds, in terms of the entropy of parent distribution, for the entropy of current records are obtained. It is shown that mutual information, as well as Kullback–Leibler distance between the endpoints of record coverage, Kullback–Leibler distance between data distribution, and current records, are all distribution-free.     

Conditional Information in Projections of Gaussian Vectors

Conditional information measures the information in a sample for an interest parameter in the presence of nuisance parameter. In the context of Gaussian likelihoods this paper first derives conditions under which a projection of the data may reduce conditional information to zero. These are then applied in the context of time series regressions, and inference on a covariance parameter, such as with either autoregressive or moving average errors. It is shown that regressing out very common regressors, such as a linear trend or dummy variable, can imply that conditional information is zero in the case of non-stationary autoregressions or non-invertible moving averages, respectively.     

Statistical analysis of a two-unit dependent repairable system

Maximum likelihood estimators are investigated a for lr-out-of 2:G repairable system when failures and repairs are statistically dependent. Under two censoring schemes Accelerated Life Testing Procedure (ALTP) is used to obtain the estimates. Information matrices are supplied and a special case when the failure and repair phenomenon are independent of each other is considered.