Statistics

A weighted model based on the Rayleigh distribution is proposed and the statistical and reliability properties of this model are presented. Some non-Bayesian and Bayesian methods are used to estimate the β parameter of proposed model. The Bayes estimators are obtained under the symmetric (squared error) and the asymmetric (linear exponential) loss functions using non-informative and reciprocal gamma priors. The performance of the estimators is assessed on the basis of their biases and relative risks under the two above-mentioned loss functions. A simulation study is constructed to evaluate the ability of considered estimation methods. The suitability of the proposed model for a real data is shown by using the Kolmogorov-Smirnov goodness-of-fit test.

A new four parameter extreme value distribution is defined and studied. Various structural properties of the proposed distribution including ordinary and incomplete moments, generating functions, residual and reversed residual life functions, order statistics are investigated. Some useful characterizations based on two truncated moments as well as based on the reverse hazard function and on certain functions of the random variable are presented. The maximum likelihood method is used to estimate the model parameters. Further, we propose a new extended regression model based on the logarithm of the new distribution. The new distribution is applied to model three real data sets to prove empirically its flexibility.

In this work, we introduce a new class of continuous distributions called the generalized Poisson family which extends the quadratic rank transmutation map. We provide some special models for the new family. Some of its mathematical properties including Rényi and q-entropies, order statistics and characterizations are derived. The estimations of the model parameters are performed by maximum likelihood method. The Monte Carlo simulation is used for assessing the performance of the maximum likelihood estimators. The flexibility of the proposed family is illustrated by means of two applications to real data sets.

In this paper, we investigate a new model based on Burr X and Fréchet distribution forextreme values and derive some of its properties. Maximum likelihood estimation alongwith asymptotic confidence intervals is considered for estimating the parameters of thedistribution. We demonstrate empirically the flexibility of the distribution in modelingvarious types of real data. Furthermore, we also provide Bayes estimators and highestposterior density intervals of the parameters of the distribution using Markov ChainMonte Carlo (MCMC) methods.

In this paper, we study a goodness-of-fit (GOF) test in the presence of lengthbiased sampling. For this purpose, we introduce a smoothed estimator of distribution function and we investigate its asymptotic behaviors, such as uniform consistency and asymptotic normality. Based on this estimator we define a one sample Kolmogorov type of GOF test for length-biased data. We conduct Monte Carlo simulations to evaluate the performance of the proposed test statistic and compare it with the one sample Kolmogorov type of GOF test obtained by the non-smoothed estimator of distribution function.

In this paper, we introduce a new goodness-of-fit test for Rayleigh distribution based on Hellinger distance. In addition, some properties about the proposed test is presented. Then, new proposed test is compared with other goodness-of-fit tests for Rayleigh distribution in the literature in terms of power. Finally, we conclude that the entropy based tests demonstrate a good performance in terms of power and we can choose the Hellinger test as more powerful than the other competitor tests.

In this work, we introduce a new class of continuous distributions called the generalized poissonfamily which extends the quadratic rank transmutation map. We provide some special models for thenew family. Some of its mathematical properties including Rényi and q-entropies, order statistics andcharacterizations are derived. The estimations of the model parameters is performed by maximumlikelihood method. The Monte Carlo simulations is used for assessing the performance of the maximumlikelihood estimators. The ‡exibility of the proposed family is illustrated by means of two applicationsto real data sets.

We propose a new class of continuous models called the Weibull Generalized G family with two extra positive shape parameters, which extends several well-known models. We obtain some of its mathematical properties including ordinary and incomplete moments, generating function, order statistics, probability weighted moments, entropies, residual, and reversed residual life functions. Characterizations based on a ratio of two truncated moments, in terms of hazard function and based on certain functions of the random variable are presented. We estimate the model parameters by the maximum likelihood method. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of two simulation studies. The usefulness of the proposed models is illustrated via three real data sets.

Recently, Sati and Gupta [1] have introduced a generalized cumulative residual entropy based on the non-additive Tsallis entropy. The cumulative residual entropy, introduced by Rao et al. [2] is a generalized measure of uncertainty which is applied in reliability and image alignment and non-additive measures of entropy. This entropy finds justifications in many physical, biological and chemical phenomena. In this paper, we derive the weighted form of this measure and call it Weighted Cumulative Residual Tsallis Entropy (WCRTE). Being a "lengthbiased" shift-dependent information measure, WCRTE is related to the differential information in which higher weight is assigned to large values of observed random variables. Based on the dynamic version of this new information measure, we propose ageing classes and it is shown that it can uniquely determine the survival function and Rayleigh distribution. Several properties, including linear transformations, bounds and related results to stochastic orders are obtained for these measures. Also, we identify classes of distributions in which some well-known distributions are maximum dynamic version of WCRTE. The empirical WCRTE is finally proposed to estimate the new information measure.

A new class of models called the transmuted odd log-logistic-G family IS proposed and studied. The method of maximum likelihood is used to estimate the unknown parameters. The performance of the maximum likelihood estimators is assessed in terms of biases and mean squared errors by means of three simulation studies. The usefulness of the proposed family is illustrated by using three real data sets

In this paper, we propose a test for the null hypothesis that a decreasing density function belongs to a givenparametric family of distribution functions against the non-parametric alternative. This method, which is based on an empirical likelihood (EL) ratio statistic, is similar to the test introduced by Vexler and Gurevich [23]. The consistency of the test statistic proposed is derived under the null and alternative hypotheses. A simulation study is conducted to inspect the power of the proposed test under various decreasing alternatives. In each scenario, the critical region of the test is obtained using a Monte Carlo technique. The applicability of the proposed test in practice is demonstrated through a few real data examples.  

A weighted model based on the Rayleigh distribution is proposed and the statistical and reliability properties of this model are presented. Some non-Bayesian and Bayesian methods are used to estimate the β parameter of proposed model. The Bayes estimators are obtained under the symmetric (squared error) and the asymmetric (linear exponential) loss functions using non-informative and reciprocal gamma priors. The performance of the estimators is assessed on the basis of their biases and relative risks under the two above-mentioned loss functions. A simulation study is constructed to evaluate the ability of considered estimation methods. The suitability of the proposed model for a real data is shown by using the Kolmogorov-Smirnov goodness-of-fit test.

In the literature, several continuous univariate distributions have been extensively used for modeling data in many areas such as economics, engineering, biological studies and environmental sciences. However, applied areas such as …nance, lifetime analysis and insurance clearly require extended forms of these distributions. So, several classes of distributions have been constructed by extending common families of continuous distributions. These generalized distributions give more ‡exibility by adding one "or more" parameters to the baseline model. They were pioneered by Gupta et al. (1998) who proposed the exponentiated-G class, which consists of raising the cumulative distribution function (cdf) to a positive power parameter. Many other classes can be cited such as the Marshall-Olkin-G family by Marshall and Olkin (1997), beta generalized-G family by Eugene et al. (2002), exponentiated generalized-G family by Cordeiro et al. (2013), a new method for generating families of continuous distributions by Alzaatreh et al. (2013), transmuted exponentiated generalized-G by Yousof et al. (2015), exponentiated transmuted-G by Merovc et al. (2016), Burr X-G by Yousof et al. (2016), transmuted Weibull G family by Alizadeh et al. (2016), complementary generalized transmuted Poisson-G family by Alizadeh et al. (2016b), transmuted geometric-G by A…fy et al. (2016a), complementary geometric transmuted-G family A…fy et al. (2016b), Kumaraswamy transmuted-G by A…fy et al. (2016c), exponentiated generalized-G Poisson by Aryal and Yousof (2017), Marshall-Olkin generalized family by Yousof et al. (2017a), beta Weibull-G family of distributions by Yousof et al. (2017b), Type I general exponential class of distributions by Hamedani et al. (2017), Topp-Leone odd log-logistic family by de Brito et al. (2017), generalized odd generalized exponential family by Alizadeh et al. (2017), exponentiated Weibull-H family Cordeiro et al. (2017a), generalized transmuted-G by Nofal et al. (2017), Burr XII system of densities by Cordeiro et al. (2017b) and beta transmuted-H family by A…fy et al. (2017), among others.

A new four parameter extreme value distribution is defined and studied. Various structural properties of the proposed distribution including ordinary and incomplete moments, generating functions, residual and reversed residual life functions, order statistics are investigated. Some useful characterizations based on two truncated moments as well as based on the reverse hazard function and on certain functions of the random variable are presented. The maximum likelihood method is used to estimate the model parameters. Further, we propose a new extended regression model based on the logarithm of the new distribution. The new distribution is applied to model three real data sets to prove empirically its flexibility.

This paper uses inequality-measurement techniques to assess goodness of fit in income distribution models. It exposes the shortcomings of the use of conventional goodness of fit criteria in face of the big income data and proposes a new set of metrics, based on income inequality curves. In this note, we mentioned that the distance between theoretical and empirical inequality curves can be considered as a goodness of fit criterion. We demonstrate certain advantages of this measure over the other general goodness of fit criteria. Unlike other goodness of fit measures, this criterion is bounded. It is 0 in minimum difference and 1 in maximum distance. Furthermore, there is a consistency between this new goodness of fit measure and the other conventional criteria. A simulation study based on fitted distribution to real income data is performed in order to investigate some statistical properties of the new goodness of fit measure. An empirical study and comparisons are also provided.

The present study aimed at investigating the long-term degradation of vegetation in Baluchistan in southwest Asia. To achieve the objective NDVI products of the MODIS sensor on Terra Satellite (MOD13A3) with spatial resolution of 1×1 km for a period of 16 years (2000-2015) were used. After obtaining images from the NASA land processes distributed active archive center, all images downloaded for the study area were mosaicked and referenced by Universal Transverse Mercator Project System and by using the nearest-neighbour re-sampling method. Then, on a pixel-based scale, the trend of long-term changes in vegetation was studied using the seasonal Mann-Kendall non-parametric test. The results show that 1.23% of the total area under study had a long-term decreasing trend in vegetation. Out of this 1.23%, 0.33% were significant at a probability level of α = 0.01, 0.24% was significant at a probability level of α = 0.05, and 0.12% were significant at a probability level of α = 0.1. The decreasing trend of 0.54% of them was not confirmed at any of the significant levels. Among the various types of vegetation, shrublands and croplands had the most significant long-term decreasing changes, which could be dangerous signs of ecotones degradation as well as weakening the sustainable rural livelihoods in this land.

Land use and land cover (LULC) changes have been one of the most important and persistent factors recently causing changes in the Earth's land. The present study aimed to detect land use and land cover (LULC) changes in Baluchistan, in Southwestern Asia, which is shared by the three countries of Iran, Pakistan, and Afghanistan, using satellite remote-sensing products. To this end, the global land cover classification provided for a period of 13 years from 2001 to 2013 by the MODIS Land Cover Type product (MCD12Q1) was used. The changes and dynamics of different land cover classes were investigated using net change analysis and cross-tabulating matrix analysis methods. The net change analysis showed that the most area of Baluchistan is covered by the barren or sparsely vegetated land cover (about 82%) and the shrubland (about 16%) classes. The dynamics analysis of different land cover classes also indicated that there were almost mutually inverse relationships between the different land cover classes in Baluchistan. Such mutual relationships were most common between the following pair classes: shrublands-bare and non-vegetated lands; grasslands-bare and non-vegetated land classes; croplands-bare and nonvegetated lands classes; and shrublands-grasslands. The most unstable land cover classes in this territory were forests, Savannas, and grassland classes. Also, the analysis of land cover changes in the period 2001-2013 provided no clear and accurate evidence of desertification and land degradation at this spatial scale in Baluchistan.

The authors have retracted this article. After publication, concerns were raised regarding overlap between this article and a previous publication from a different author group . Specifically, Sect. 3.3, including the "New method", comparison between "Former method" and "New method", and Fig. are reused from [1] without appropriate attribution. The authors have stated that they based this section on the previous article and have agreed that they should have been more explicit about the reuse of materials.

Simple nonparametric estimates of the conditional distribution of a response variable given a covariate are often useful for data exploration purposes or to help with the specification or validation of a parametric or semi-parametric regression model. In this paper we propose such an estimator in the case where the response variable is interval-censored and the covariate is continuous. Our approach consists in adding weights that depend on the covariate value in the self-consistency equation proposed by Turnbull (J R Stat Soc Ser B 38:290-295, 1976), which results in an estimator that is no more difficult to implement than Turnbull's estimator itself. We show the convergence of our algorithm and that our estimator reduces to the generalized Kaplan-Meier estimator (Beran, Nonparametric regression with randomly censored survival data, 1981) when the data are either complete or right-censored. We demonstrate by simulation that the estimator, bootstrap variance estimation and bandw...