Minimum variance unbiased estimation in natural exponential families generated by stable distributions

The class of nature exponential families generated by stable distributions has been introduced in different contexts by several authors. Tweedie (1984) and Jorgensen (1987) studied this class in the context of generalized liner models and exponential dispersion models. Bar-Lev and Enis (1986) introduced this class in the context of the property of reproducibility in natural exponential families and Hougaard (1986) found the distributions in this class to be natural candidates for applications as survival distributions in life tables for heterogeneous populations. In this note, we consider such a class in the context of minimum variance unbiased estimation. For each family in this class, we obtain an explicit expression for the uniformly minimum variance unbiased estimator for the r-th cumlant, the density function, and the reliability function.     

New class of location-parameter discrete probability distributions and their characterizations

A new class of location-parameter discrete probability distributions (LDPD) has been defined where the population mean is the location parameter. It has been shown that some single parameter discrete distributions do not belong to this class and all discrete probability distributions belonging to this class can be characterized by their variances only. Expressions are given for the first four central moments and a recurrence formula for higher central moments has been obtained. Eight theorems are given to characterize the various distributions in the LDPD class.     

Good item or bad—can latent class analysis tell?: the utility of latent class analysis for the evaluation of survey questions

Summary.  Latent class analysis has been used to model measurement error, to identify flawed survey questions and to estimate mode effects. Using data from a survey of University of Maryland alumni together with alumni records, we evaluate this technique to determine its usefulness for detecting bad questions in the survey context. Two sets of latent class analysis models are applied in this evaluation: latent class models with three indicators and latent class models with two indicators under different assumptions about prevalence and error rates. Our results indicated that the latent class analysis approach produced good qualitative results for the latent class models—the item that the model deemed the worst was the worst according to the true scores. However, the approach yielded weaker quantitative estimates of the error rates for a given item.     

Stochastic ordering and a class of multivariate new better than used distributions

A new characterization for the univariate class of new better than used ‘NBU’ distributions in terms of stochastic ordering is introduced. A multivariate version of this characterization is then used to define a multivariate class of NBU distributions. Basic properties of this class are derived. Comparisons and relationships of this new class with earlier classes are developed. Two multivariate new worse than used (NWU) classes of life distributions are defined and compared and their basic properties are studied.     

The compound class of linear failure rate-power series distributions: Model,properties, and applications

In this article, a new class of distributions is introduced, which generalizes the linear failure rate distribution and is obtained by compounding this distribution and power series class of distributions. This new class of distributions is called the linear failure rate-power series distributions and contains some new distributions such as linear failure rate-geometric, linear failure rate-Poisson, linear failure rate-logarithmic, linear failure rate-binomial distributions, and Rayleigh-power series class of distributions. Some former works such as exponential-power series class of distributions, exponential-geometric, exponential-Poisson, and exponential-logarithmic distributions are special cases of the new proposed model. The ability of the linear failure rate-power series class of distributions is in covering five possible hazard rate function, that is, increasing, decreasing, upside-down bathtub (unimodal), bathtub and increasing-decreasing-increasing shaped. Several properties of this class of distributions such as moments, maximum likelihood estimation procedure via an EM-algorithm and inference for a large sample, are discussed in this article. In order to show the flexibility and potentiality, the fitted results of the new class of distributions and some of its submodels are compared using two real datasets.     

Optimal cut-off for rare events and unbalanced misclassification costs

This paper develops a method for handling two-class classification problems with highly unbalanced class sizes and misclassification costs. When the class sizes are highly unbalanced and the minority class represents a rare event, conventional classification methods tend to strongly favour the majority class, resulting in very low detection of the minority class. A method is proposed to determine the optimal cut-off for asymmetric misclassification costs and for unbalanced class sizes. Monte Carlo simulations show that this proposal performs better than the method based on the notion of classification accuracy. Finally, the proposed method is applied to empirical data on Italian small and medium enterprises to classify them into default and non-default groups.     

An extended class of permutation techniques for matched pairs

A class of matched-pairs permutation techniques based on distances between each pair of observed signed values is considered. Although many commonly-used inference techniques for matched pairs are members of this class, some of the more appealing inference techniques among this class have received very little attention. Two new simple rank tests of this class jointly possess both intuitive properties and location-alternative power characteristics which appear more appealing than the corresponding characteristics of either the sign test or the Wllcoxon signed-ranks test. In particular, power comparisons based on slmula-tions indicate that these new rank tests are jointly as good or even vastly superior to the sign test or the Wilcoxon signed-ranks test for location alternatives involving five symmetric distributions. The five distributions selected for these com-parisons include the Laplace, logistic, normal, uniform and a U-shaped distribution     

Generalized Weighted Exponential Distribution

The new class of weighted exponential (WE) distributions obtained by Gupta and Kundu (2009) by implementing Azzalini's method to the exponential distribution. In this study, we generalize the WE distribution to a new class of generalized weighted exponential (GWE) distribution. Several statistical and reliability properties of this new class of distribution are obtained. Estimation and inference procedure for distribution parameters are investigated. Finally, we show that the proposed model can provide better fit than the recent class of weighted exponential by using two real data examples.     

Permutation techniques for analyzing multi-response data from randomized block experiments

A class of permutation techniques is presented for the randomized block design. This class is specifically devised for analyses involving multivariate data. A numerical example illustrates an application based on multivariate data. Many well known techniques are special cases of this class. Among these special cases are (i) the permutation version of the classical univariate technique for randomized blocks which 1s associated with analysis of variance, (ii) the Friedman randomized block test, (iii) one-sample matched-pair tests, (iv) the Pearson correlation measure, and (v) the Spearman rank correlation and foot-rule measures. Furthermore, variations and multivariate versions among this class suggest a variety of new techniques which have not received any previous attention.     

SOME RESULTS ON TRUNCATION DEPENDENCE INVARIANT CLASS OF COPULAS

ABSTRACT

In this paper, m-dimensional distribution functions with truncation invariant dependence structure are studied. Some of the properties of generalized Archimedean class of copulas under this dependence structure are presented including some results on the conditions of compatibility. It has been shown that Archimedean copula generalized as it is described by Jouini and Clemen[1] Jouini, M.N. and Clemen, R.T. 1996. Copula Models for Aggregating Expert Opinions. Operations Research, 44(3): 444–457.  [Google Scholar] which has the truncation invariant dependence structure has to have the form of independence or Cook-Johnson copula. We also consider a multi-parameter class of copulas derived from one-parameter Archimedean copulas. It has been shown that this class has a probabilistic meaning as a connecting copula of the truncated random pair with a right truncation region on the third variable. Multi-parameter copulas generated in this paper stays in the Archimedean class. We provide formulas to compute Kendall's tau and explore the dependence behavior of this multi-parameter class through examples.     

Using a GLM to Decompose the Symmetry Model in Square Contingency Tables with Ordered Categories

In this paper, we are employing the generalized linear model (GLM) in the form 𝓁_ij=Xλ to decompose the symmetry model into the class of models discussed in Tomizawa (1992 Tomizawa, S. 1992. Quasi-diagonals-parameter symmetry model for square contingency tables with ordered categories. Calcutta Statist. Assoc. Bull., 39: 53–61.  [Google Scholar]). In this formulation, the random component would be the observed counts f _ij with an underlying Poisson distribution. This approach utilizes the non-standard log-linear model and our focus in this paper therefore relates to models that are decompositions of the complete symmetry model. That is, models that are implied by the symmetry models. We develop factor and regression variables required for the implementation of these models in SAS PROC GENMOD and SPSS PROC GENLOG. We apply this methodology to analyse the three 4×4 contingency table, one of which is the Japanese Unaided distance vision data. Results obtained in this study are consistent with those from the numerous literature on the subject. We further extend our applications to the 6×6 Brazilian social mobility data. We found that both the quasi linear diagonal-parameters symmetry (QLDPS) and the quasi 2-ratios parameter symmetry (Q2RPS) models fit the Brazilian data very well. Parsimonious models being the QLDPS and the quasi-conditional symmetry (QCS) models. The SAS and SPSS programs for implementing the models discussed in this paper are presented in Appendices A, B and C.     

A Class of Sampling Two Units with Probability Proportional to Size

A class of sampling two units without replacement with inclusion probability proportional to size is proposed in this article. Many different well known probability proportional to size sampling designs are special cases from this class. The first and second inclusion probabilities of this class satisfy important properties and provide a non-negative variance estimator of the Horvitz and Thompson estimator for the population total. Suitable choice for the first and second inclusion probabilities from this class can be used to reduce the variance estimator of the Horvitz and Thompson estimator. Comparisons between different proportional to size sampling designs through real data and artificial examples are given. Examples show that the minimum variance of the Horvitz and Thompson estimator obtained from the proposed design is not attainable for the most cases at any of the well known designs.     

Multivariate tail conditional expectation for scale mixtures of skew-normal distribution

In practice, a financial or actuarial data set may be a skewed or heavy-tailed and this motivates us to study a class of distribution functions in risk management theory that provide more information about these characteristics resulting in a more accurate risk analysis. In this paper, we consider a multivariate tail conditional expectation (MTCE) for multivariate scale mixtures of skew-normal (SMSN) distributions. This class of distributions contains skewed distributions and some members of this class can be used to analyse heavy-tailed data sets. We also provide a closed form for TCE in a univariate skew-normal distribution framework. Numerical examples are also provided for illustration.     

Refining binomial confidence intervals

A method for refining an equivariant binomial confidence procedure is presented which, when applied to an existing procedure, produces a new set of equivariant intervals that are uniformly superior. The family of procedures generated from this method constitute a complete class within the class of all equivariant procedures. In certain cases it is shown that this class is also minimal complete. Also, an optimally property, monotone minimaxity, is investigated, and monotone minimax procedures are constructed.     

ASYMPTOTIC POSTERIOR NORMALITY FOR STOCHASTIC PROCESSES: A NON-ERGODIC EXAMPLE

Sweeting & Adekola (1987) presented a fairly general set of conditions, covering a wide class of problems, that establish asymptotic posterior normality for stochastic processes. In this paper, this theory is illustrated via a non-ergodic example, namely, the class of non-homogeneous birth processes.     

Further results on the two-stage hierarchial information (2shi) estimators in the linear regression models

The paper considers a class of 2SHI estimators for the linear regression models and provides some results regarding the dominance in quadratic loss of this class over the OLS and usual Stein-rule estimators.     

A Bayesian approach to Weibull survival models—Application to a cancer clinical trial

In this paper we outline a class of fully parametric proportional hazards models, in which the baseline hazard is assumed to be a power transform of the time scale, corresponding to assuming that survival times follow a Weibull distribution. Such a class of models allows for the possibility of time varying hazard rates, but assumes a constant hazard ratio. We outline how Bayesian inference proceeds for such a class of models using asymptotic approximations which require only the ability to maximize the joint log posterior density. We apply these models to a clinical trial to assess the efficacy of neutron therapy compared to conventional treatment for patients with tumors of the pelvic region. In this trial there was prior information about the log hazard ratio both in terms of elicited clinical beliefs and the results of previous studies. Finally, we consider a number of extensions to this class of models, in particular the use of alternative baseline functions, and the extension to multi-state data.     

On a measure of dependence based on fisher's information matrix

A class of measures of dependence between two random vectors is defined, in terms of the canonical correlations obtained from Fisher's information matrix. Some basic properties are proved for this class of measures. Examples are given to illustrate that the class gives good measures, under normal models. Interesting measures are also arise for bivariate models where the correlation coefficient does not exist for some values of the parameters of the model.     

Some Results on Fractional Factorial Split-Plot Designs with Multi-Level Factors

Fractional factorial split-plot (FFSP) designs have received much attention in recent years. In this article, the matrix representation for FFSP designs with multi-level factors is first developed, which is an extension of the one proposed by Bingham and Sitter (1999b Bingham , D. , Sitter , R. R. ( 1999b ). Some theoretical results for fractional factorial split-plot designs . Ann. Statist. 27 : 1240 – 1255 . [Google Scholar]) for the two-level case. Based on this representation, periodicity results of maximum resolution and minimum aberration for such designs are derived. Differences between FFSP designs with multi-level factors and those with two-level factors are highlighted.