Gamze Özel

The probability function of a geometric Poisson distribution

The geometric Poisson (also called Pólya–Aeppli) distribution is a particular case of the compound Poisson distribution. In this study, the explicit probability function of the geometric Poisson distribution is derived and a straightforward proof for this function is given. By means of a proposed algorithm, some numerical examples and an application on traffic accidents are also given to illustrate the usage of the probability function and proposed algorithm.

The generalized odd log-logistic family of distributions: properties, regression models and applications

ABSTRACT We propose a new class of continuous distributions with two extra shape parameters named the generalized odd log-logistic family of distributions. The proposed family contains as special cases the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Some of its mathematical properties including ordinary moments, quantile and generating functions, two entropy measures and order statistics are obtained. We derive a power series for the quantile function. We discuss the method of maximum likelihood to estimate the model parameters. We study the behaviour of the estimators by means of Monte Carlo simulations. We introduce the log-odd log-logistic Weibull regression model with censored data based on the odd log-logistic-Weibull distribution. The importance of the new family is illustrated using three real data sets. These applications indicate that this family can provide better fits than other well-known classes of distributions. The beauty and importance of the proposed family lies in its ability to model different types of real data.

Survival functions for the frailty models based on the discrete compound Poisson process

Frailty models are often used to model heterogeneity in survival analysis. The distribution of the frailty is generally assumed to be continuous. In some circumstances, it is appropriate to consider discrete frailty distributions. Having zero frailty can be interpreted as being immune, and population heterogeneity may be analysed using discrete frailty models. In this paper, survival functions are derived for the frailty models based on the discrete compound Poisson process. Maximum likelihood estimation procedures for the parameters are studied. We examine the fit of the models to earthquake and the traffic accidents’ data sets from Turkey.

A new modified Jackknifed estimator for the Poisson regression model

ABSTRACT The Poisson regression is very popular in applied researches when analyzing the count data. However, multicollinearity problem arises for the Poisson regression model when the independent variables are highly intercorrelated. Shrinkage estimator is a commonly applied solution to the general problem caused by multicollinearity. Recently, the ridge regression (RR) estimators and some methods for estimating the ridge parameter k in the Poisson regression have been proposed. It has been found that some estimators are better than the commonly used maximum-likelihood (ML) estimator and some other RR estimators. In this study, the modified Jackknifed Poisson ridge regression (MJPR) estimator is proposed to remedy the multicollinearity. A simulation study and a real data example are provided to evaluate the performance of estimators. Both mean-squared error and the percentage relative error are considered as the performance criteria. The simulation study and the real data example results show that the proposed MJPR method outperforms the Poisson ridge regression, Jackknifed Poisson ridge regression and the ML in all of the different situations evaluated in this paper.

The odd log-logistic Lindley Poisson model for lifetime data

ABSTRACT We define two new lifetime models called the odd log-logistic Lindley (OLL-L) and odd log-logistic Lindley Poisson (OLL-LP) distributions with various hazard rate shapes such as increasing, decreasing, upside-down bathtub, and bathtub. Various structural properties are derived. Certain characterizations of OLL-L distribution are presented. The maximum likelihood estimators of the unknown parameters are obtained. We propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest has a Poisson distribution and the time to event has an OLL-L distribution. The applicability of the new models is illustrated by means real datasets.

Modeling destructive earthquake casualties based on a comparative study for Turkey

The statistical modeling of destructive earthquakes is an indispensable tool for extracting information for prevention and risk reduction casualties after destructive earthquakes in a seismic region. The linear regression (LR) model can reveal the relation between casualty rate and related covariates based on earthquake catalog. However, if some covariates affect the casualty rate parametrically and some of them nonparametrically, the LR model may entail serious bias and loss of power when estimating or making inference about the effect of parameters. We suggest that semi-parametric beta regression (SBR), semi-parametric additive regression (SAR), and beta regression (BR) models could provide a more suitable description than the LR model to analyze the observed casualties after destructive earthquakes. We support this argument using destructive earthquakes occurred in Turkey between 1900 and 2012 having surface wave magnitudes five or more. The LR, SAR, BR, and SBR models are compared within the context of this data. The data strongly support that the SBR and SAR models can lead to more precise results than the BR and LR models. Furthermore, the SBR is the best model for the earthquake data since the beta distribution provides a flexible model that can be used to analyze the data involving proportions or rates. The results from this model suggest that the casualty rate depends on energy, damaged buildings, and the number of aftershocks of a destructive earthquake.

The odd log-logistic Marshall-Olkin power Lindley Distribution: Properties and applications

Abstract In this paper, we introduce a new extension of the power Lindley distribution, called the odd log-logistic Marshall-Olkin power Lindley distribution. We discuss some of its properties such as the shapes of the density, hazard rate functions, quantile function, mixture representation, moments, and order statistics. We also obtain the estimators of the parameters through maximum likelihood approach. A simulation study is performed to evaluate the performance of the maximum likelihood estimators. Finally, two real data sets are applied to illustrating of the usefulness of the new model and to comparing the fit of the new distribution with those attained by some other extensions of the Lindley and power Lindley distributions.

Exponential estimators using characteristics of Poisson distribution: An application to earthquake data

In this study, we have considered ratio and product exponential estimators of Poisson distributed population in simple random sampling (SRS). The mean square error (MSE) equations of the proposed estimators are obtained and compared in application with the classical ratio estimator. The findings are supported by a numerical illustration with earthquake data of Turkey.

A new generalized Poisson Lindley distribution

Probability distributions are commonly used for describing and modeling data in several different areas. There are a lot of well-known statistical distributions however they are inefficient for modeling data in many applied areas such as lifetime analysis, finance and insurance. The selection of the appropriate probability density distribution reduces the estimation error and also allows obtaining characteristics. Hence, there is a clear need for more flexible distributions. In this study, we propose a new probability distribution to model different data sets. After defining the new probability distribution named Poisson-Lindley (PL) distribution, an application to real data demonstrates that the new distribution can provide a better fit than other classical models.

Assessing the influence of climate change characteristics on the rainfall duration of Turkey

Climate change alters the rainfall patterns and causes insufficient rainfalls and irregular rainfall periods in Turkey. The reduction in rainfalls decreases the water resources in Turkey, and drought seems to be an inescapable end. This paper proposes a log-logistic accelerated failure time model with frailty to determine influence of some covariates. For this aim, we use the rainfall data from 70 meteorological stations of Turkey during 2012–2013. The survival models are compared by means of this data as a risk assessment tool in time to wet season and rainfall probability estimations. The data present that the log-logistic accelerated model is more suitable than the other survival models. The log-logistic accelerated model results show that duration time of rainfall depends on the temperature and the ratio of forest area.