Some Results on Modeling Biological Sequences and Web Navigation with a Semi Markov Chain

In the article, the entrance probabilities and the probability distribution of the number of transitions to a state are studied to provide some answers to questions related to state occupancies for the semi Markov model. Biological sequences and Web navigation are two cases that initially seem to be different but to a certain extent they do have similarities. Two main aspects of word occurrences in biological sequences are: (a) where do they occur and (b) how many times do they occur. In Web navigation the similar questions are (a) when a node is visited and (b) how many times a node is visited. So, the theoretical results of this study are applied to model these two cases and derive distributions of word location or node occurrence and frequency of occurrences. Rewards/costs are included in the Web navigation model and analytic forms for the means, variances, and moments of total interval rewards/costs are provided.     

Depth Measures for Multivariate Functional Data

In this article, we address the problem of mining and analyzing multivariate functional data. That is, data where each observation is a set of possibly correlated functions. Complex data of this kind is more and more common in many research fields, particularly in the biomedical context. In this work, we propose and apply a new concept of depth measure for multivariate functional data. With this new depth measure it is possible to generalize robust statistics, such as the median, to the multivariate functional framework, which in turn allows the application of outlier detection, boxplots construction, and nonparametric tests also in this more general framework. We present an application to Electrocardiographic (ECG) signals.     

Effective Rotation Patterns Under Non Response in Two-Occasion Successive Sampling

This article intends to develop some effective rotation patterns with the aid of attractive imputation methods when the problems of non response occur in two-occasion successive sampling. Utilizing the information on p (p ??1) auxiliary variables regression methods of imputation have been considered and subsequently multiple linear regression type estimators are proposed to estimate the current population mean in two-occasion successive sampling. Proposed estimators are compared with the estimator for same situations but in the absence of non-response. Optimum replacement strategies of the respective estimators have been discussed and results are interpreted with the help of empirical studies. Conclusions and suitable recommendations are made.     

Maximal Invariant and Weakly Equivariant Estimators

Equivariant functions can be useful for constructing of maximal invariant statistic. In this article, we discuss construction of maximal invariants based on a given weakly equivariant function under some additional conditions. The theory easily extends to the case of two or more weakly equivariant functions. Also, we derive a maximal invariant statistic when the group contains a sharply transitive and a characteristic subgroup. Finally, we consider the independence of invariant and weakly equivariant functions under some special conditions.     

Some Properties of Weighted Distributions in the Context of Repairable Systems

ABSTRACT

In this article we introduce some structural relationships between weighted and original variables in the context of maintainability function and reversed repair rate. Furthermore, we prove some characterization theorems for specific models such as power, exponential, Pareto II, beta, and Pearson system of distributions using the relationships between the original and weighted random variables.     

Estimators for the Finite Mixture of Rayleigh Model Based on Progressively Censored Data

In this article, based on progressively Type-II censored samples from a heterogeneous population that can be represented by a finite mixture of two-component Rayleigh lifetime model, the problem of estimating the parameters and some lifetime parameters (reliability and hazard functions) are considered. Both Bayesian and maximum likelihood estimators are of interest. A class of natural conjugate prior densities is considered in the Bayesian setting. The Bayes estimators are obtained using both the symmetric (squared error) loss function, and the asymmetric (LINEX and General Entropy) loss functions. It has been seen that the estimators obtained can be easily evaluated for this type of censoring by using suitable numerical methods. Finally, the performance of the estimates have been compared on the basis of their simulated maximum square error via a Monte Carlo simulation study.     

Interval Partitioning Arising from Size-Biased Picking

We consider the following fragmentation model of the unit interval 𝕀. We start fragmenting 𝕀 into two pieces with uniform random sizes. One of these two subintervals is then chosen at random according to a β-size-biased picking procedure, β ∈ ?. This particular tagged fragment is next broken into two random pieces, one of which is chosen accordingly at random for further splitting; the process is then iterated independently. This model constitutes a recursive β-partitioning procedure where splitting occurs only at one of the two fragments formed in the previous step of fragmentation. We investigate some statistical features of this model.     

A Note on Influence Assessment in Score Tests

Recently, [1] Ebrahimi, N. 1996. How to measure uncertainty about residual life time. Sankhya Ser. A, 58: 48–57.  [Google Scholar] proposed a dynamic measure based on differential entropy applied to the residual lifetime. This measure has been used for the classification and ordering of survival functions. More recently, [2] Ebrahimi, N. 1997. Testing whether lifetime distribution is decreasing uncertainty. Journal of Statistical Planning and Inference, 64: 9–19. [Crossref], [Web of Science ®] , [Google Scholar] has considered the problem of testing the monotonicity of this measure. We propose and study several kernel type estimators of the entropy of residual life through the estimation of f(x) log f(x). These estimators can be applied to the classification and comparison of lifetime distribution.