Statistica 2021-10-26T11:04:36+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. Polynomial Columns-Parameter Symmetry Model and its Decomposition for Square Contingency Tables 2021-03-30T09:48:15+02:00 Shuji Ando <p>This study proposes a polynomial columns-parameter symmetry model for square contingency tables with the same row and column ordinal classifications. In the proposed model, the odds for all i &lt; j that an observation will fall in row category i and column category j instead of row category j and column category i depend on only the value of column category j . The proposed model is original because many asymmetry models in square contingency tables depend on the both values of row and column category. The proposed model constantly holds when the columns-parameter symmetry model holds; but the converse does not necessarily hold. This study shows that it is necessary to satisfy the polynomial columns-marginal symmetry model, in addition to the columns-parameter symmetry model, to satisfy the proposed model. This decomposition theorem is useful for explaining why the proposed model does not hold. Moreover, this study shows the value of likelihood ratio chi-square statistic for testing the proposed model is equal to the sum of that for testing the decomposed two models.</p> 2021-10-26T00:00:00+02:00 Copyright (c) 2021 Statistica A New Discrete Distribution: Properties, Characterizations, Modeling Real Count Data, Bayesian and Non-Bayesian Estimations 2021-07-02T14:57:45+02:00 Haitham Mosad Yousof Christophe Chesneau Gholamhossein Hamedani Mohamed Ibrahim <p>In this work, a new discrete distribution which includes the discrete Burr-Hatke distribution is defined and studied. Relevant statistical properties are derived. The probability mass function of the new distribution can be "right skewed" with different shapes, bimodal and "uniformed". Also, the corresponding hazard rate function can be "monotonically decreasing", "upside down", "monotonically increasing", "upside down increasing", and "upside down-constant-increasing". A numerical analysis for the mean, variance, skewness, kurtosis and the index of dispersion is presented. The new distribution could be useful in the modeling of "under-dispersed" or "overdispersed" count data. Certain characterizations of the new distribution are presented. These characterizations are based on the conditional expectation of a certain function of the random variable and in terms of the hazard rate function. Bayesian and non-Bayesian estimation methods are considered. Numerical simulations for comparing Bayesian and non-Bayesian estimation methods are performed. The new model is applied for modeling carious teeth data and counts of cysts of kidneys data.</p> 2021-10-26T00:00:00+02:00 Copyright (c) 2021 Statistica Estimation of Cumulative Incidence Function in the Presence of Middle Censoring Using Improper Gompertz Distribution 2021-04-07T11:18:23+02:00 Habbiburr Rehman Navin Chandra <p>In this paper we deal with the modelling of cumulative incidence function using improper Gompertz distribution based on middle censored competing risks survival data. Together with the unknown parameters, cumulative incidence function also estimated. In classical set up, we derive the point estimates using maximum likelihood estimator and midpoint approximation methods. The asymptotic confidence interval are obtained based on asymptotic normality properties of maximum likelihood estimator. We also derive the Bayes estimates with associated credible intervals based on informative and non-informative types of priors under two loss functions such as squared error and LINEX loss functions. A simulation study is conducted for comprehensive comparison between various estimators proposed in this paper. A real life data set is also used for illustration.</p> 2021-10-26T00:00:00+02:00 Copyright (c) 2021 Statistica The Marshall-Olkin Gompertz Distribution: Properties and Applications 2021-06-01T14:09:46+02:00 Joseph Thomas Eghwerido Joel Oruaoghene Ogbo Adebola Evelyn Omotoye <p>This article introduces three parameters class for lifetime Poisson processes in the Marshall-Olkin transformation family that are increasing, bathtub and skewed. Some structural mathematical properties of the Marshall-Olkin Gompertz (MO-G) model were derived. The MO-G model parameters were established by maximum likelihood approach. The flexibility, efficiency, and behavior of the MO-G model estimators were examined through simulation. The empirical applicability, flexibility and proficiency of the MO-G model was scrutinized by a real-life dataset. The proposed MO-G model provides a better fit when compared to existing models in statistical literature and can serve as an alternative model to those appearing in modeling Poisson processes.</p> 2021-10-26T00:00:00+02:00 Copyright (c) 2021 Statistica A Class of Univariate Non-Mesokurtic Distributions Using a Continuous Uniform Symmetrizer and Chi Generator 2021-05-31T17:50:43+02:00 Kamala Naganathan Radhalakshmi Martin Luther William <p>In a good number of real life situations, the observations on a random variable of interest tend to concentrate either too closely or too thinly around a central point but symmetrically like the normal distribution. The symmetric structure of the density function appears like that of a normal distribution but the concentration of the observations can be either thicker or thinner around the mean. This paper attempts to generate a family of densities that are symmetric like normal but<br />with different kurtosis. Drawing inspiration from a recent work on multivariate leptokurtic normal distribution, this paper seeks to consider the univariate case and adopt a different approach to generate a family to be called ’univariate non-mesokurtic normal’ family.The symmetricity of the densities is brought out by a uniform random variable while the kurtosis variation is brought about by a chi generator. Some of the properties of the resulting class of distributions and the pameter estimation are discussed.</p> 2021-10-26T00:00:00+02:00 Copyright (c) 2021 Statistica