Authors:Kunnathully Unnikrishnan Nitha, Sreekrishnanilayam Devakiamma Krishnarani Pages: 365 - 382 Abstract: An autoregressive process of order one with double Lindley distribution as marginal is introduced. A mixture distribution is obtained for the innovation process. Analytical properties of the process are discussed. The parameters of the process are estimated and simulation studies are done. Practical application of the process is discussed with the help of a real data set. PubDate: 2022-03-02 DOI: 10.6092/issn.1973-2201/10411 Issue No:Vol. 81, No. 4 (2022)

Authors:Gabriele Nunzio Tornetta Pages: 383 - 398 Abstract: Many classification models produce a probability distribution as the outcome of a prediction. This information is generally compressed down to the single class with the highest associated probability. In this paper we argue that part of the information that is discarded in this process can be in fact used to further evaluate the goodness of models, and in particular the confidence with which each prediction is made. As an application of the ideas presented in this paper, we provide a theoretical explanation of a confidence degradation phenomenon observed in the complement approach to the (Bernoulli) Naïve Bayes generative model. PubDate: 2022-03-02 DOI: 10.6092/issn.1973-2201/11479 Issue No:Vol. 81, No. 4 (2022)

Authors:Abbes Rabhi, Nadia Kadiri, Sanaà Dounya Mekki Pages: 399 - 422 Abstract: The main objective of this work is to estimate, semi-parametrically, the mode of a conditional density when the response is a real valued random variable subject to censored phenomenon and the predictor takes values in a semi-metric space. We assume that the explanatory and the response variables are linked through a single-index structure. First, we introduce a type of kernel estimator of the conditional density function when the data are supposed to be selected from an underlying stationary and ergodic process with missing at random (MAR). Under some general conditions, both the uniform almost-complete consistencies with convergence rates of the model are established. Further, the asymptotic normality of the considered model is given. As an application, the asymptotic (1−α) confidence interval of the conditional density function and the conditional mode are also presented for 0 < α < 1. PubDate: 2022-03-02 DOI: 10.6092/issn.1973-2201/10472 Issue No:Vol. 81, No. 4 (2022)

Authors:Satheesh Kumar, Rakhi Ramachandran Pages: 423 - 446 Abstract: Here we develop a zero-inflated version of the alternative hyper-Poisson distribution and discuss its important statistical properties such as probability generating function, expressions for mean, variance, factorial moments, skewness, kurtosis, recursion formula for probabilities, raw moments and factorial moments. Then the maximum likelihood estimation of the parameters of the zero-inflated alternative hyper-Poisson distribution is discussed and certain test procedures are constructed for testing the significance of the inflation parameter. All the procedures are illustrated with the help of certain real life data sets. Moreover, a brief simulation study is carried out for assessing the performances PubDate: 2022-03-02 DOI: 10.6092/issn.1973-2201/9338 Issue No:Vol. 81, No. 4 (2022)

Authors:Manoj Chacko, Shiny Mathew Pages: 447 - 459 Abstract: In this paper, the problem of estimation of R = P(Y < X) based on ranked set sampling, when (X,Y) follows generalised Pareto distribution (GPD) is considered. The maximum likelihood (ML) estimators and Bayes estimators of R are obtained. A Monte Carlo simulation is also performed to study the behaviour of different estimators. PubDate: 2022-03-02 DOI: 10.6092/issn.1973-2201/10480 Issue No:Vol. 81, No. 4 (2022)