Statistica 2021-09-03T16:41:01+02:00 Simone Giannerini Open Journal Systems <strong>STATISTICA – ISSN 1973-2201</strong> is a quarterly journal, founded by Paolo Fortunati. Statistica accepts original papers dealing with methodological and technical aspects of statistics and statistical analyses in the various scientific fields. It publishes also book reviews and announcements. Full texts are available since 2002. Robust Estimations of Survival Function for Weibull Distribution 2021-04-30T09:42:55+02:00 Derya Karagöz Nihal Ata Tutkun <p>The aim of this study is to estimate the robust survival function for the Weibull distribution. Since the survival function of Weibull distribution is based on the parameters, we consider two robust and explicit Weibull parameter estimators proposed by Boudt et al. (2011). The quantile and the quantile least squares which are all robust to censored data is used as an alternative to the maximum likelihood estimation of the Weibull parameters. The proposed estimators are applied to Hodgin’s disease data which produces smaller variances for the robust survival function. The advantage of new methods is that they are numerically explicit in applications. Monte Carlo simulation is performed to compare the behaviours of the proposed robust estimators in the presence of right, left and interval censored observations considering different censoring rates. The simulation results show that the proposed robust estimators are better than the maximum likelihood estimator.</p> 2021-09-03T00:00:00+02:00 Copyright (c) 2021 Statistica Characterization of Generalized Distribution by Doubly Truncated Moment 2020-09-19T09:24:23+02:00 Haseeb Athar Yahia Abdel-Aty Mohd. Almech Ali <p>In this paper characterization properties based on conditional expectation of a continuous function of random variable are studied when truncation is from both the sides, left and right. Then, these results are applied to obtain the k-th doubly truncated moment for a general class of distribution. Further, some examples and particular cases based on this general class of distributions are also demonstrated. The results are obtained in simple and explicit manner which also unifies the earlier results obtained by several authors. In the end, simulation study is performed to validate the correctness of theoretical characterization results and then two real life data sets are used to demonstrate the applications of these results.</p> 2021-09-03T00:00:00+02:00 Copyright (c) 2021 Statistica The Zografos-Balakrishnan Lindley Distribution: Properties and Applications 2020-06-28T17:22:44+02:00 Muhammed Rasheed Irshad Veena D'cruz Radhakumari Maya <span>The Lindley distribution was proposed in the context of Bayesian statistics as a counter example of fiducial statistics. In this paper, we propose Zografos Balakrishnan Lindley (ZBL) distribution in which Lindley distribution is a special case. Some properties of the new distribution is obtained such as moments, hazard rate function, reliability function etc. The parameters are estimated using the method of maximum likelihood. Finally an application of the proposed distribution to a real data set is illustrated and it is concluded that Zogarfos Balakrishnan Lindley (ZBL) distribution provides better fit than other classical distributions.</span> 2021-09-03T00:00:00+02:00 Copyright (c) 2021 Statistica A Flexible Bathtub-Shaped Failure Time Model: Properties and Associated Inference 2020-09-18T09:18:46+02:00 Neha Choudhary Abhishek Tyagi Bhupendra Singh <p>In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contains sub-models that are widely used in lifetime data analysis such as the modified Weibull, Chen, extreme value, Weibull, Rayleigh, and exponential distributions. We study its statistical properties which include the hazard rate function, moments and distribution of the order statistics. The parameters involved in the model are estimated by using maximum likelihood and the Bayesian method of estimation. In Bayesian estimation, we assume independent Gamma priors for the parameters and MCMC technique such as the Metropolis-Hastings algorithm within Gibbs sampler has been implemented to obtain the sample-based estimators and the highest posterior density intervals of the parameters. Tierney and Kadane (1986) approximation is also used to obtain Bayes estimators of the parameters. In order to highlight the relative importance of various estimates obtained, a simulation study is carried out. The usefulness of the proposed model is illustrated using two real datasets.</p> 2021-09-03T00:00:00+02:00 Copyright (c) 2021 Statistica Muth Distribution and Estimation of a Parameter Using Order Statistics 2020-09-11T12:20:03+02:00 Muhammed Rasheed Irshad Radhakumari Maya Sasikumar Padmini Arun <p>In this work, we have considered a lifetime distribution namely Muth distribution and pointed out instances where it appears as a good model to study the stochastic nature of the variable under consideration. We have derived the best linear unbiased estimator (BLUE) of the scale parameter of the Muth distribution based on order statistics for some known values of the shape parameter.We have further estimated the scale parameter of Muth distribution by U-statistics based on best linear functions of order statistics as kernels. The efficiency of the BLUE relative to the usual unbiased estimator has been also evaluated. An illustration describing the performance of U-statistics estimation method when compared with the classical maximum likelihood method is also given.</p> 2021-09-03T00:00:00+02:00 Copyright (c) 2021 Statistica