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Introduction
My research deals with higher-order asymptotics, mathematical statistics, regression models, mortality models, and distribution theory.
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Publications
Publications (153)
We focus on the gamma-Gompertz-Makeham model, and derive useful structural properties for this mortality model. We provide the basic properties like moments, remaining life expectancy, single life annuity, among many others, in closed form, and so it eliminates the need of evaluating them through numerical integration directly. The estimation of th...
The Bell--Touchard regression model for count response variables was introduced recently in the statistical literature. This regression model for counts is, in some aspects, similar to the generalized linear model framework, and the mean response is related to covariates and unknown regression coefficients, which allows for parameter interpretation...
It is verified that the maximum likelihood (ML) estimators of the standard two‐sided power distribution (STSP) parameters introduced by van Dorp and Kotz on the interval (0,1) can be severely biased. Since the usual analytical methods of bias correction cannot be applied in such a parametric distribution, bootstrap bias correction methods are propo...
Analytic expressions for the single and joint life annuities based on the Makeham–Beard mortality law have been derived recently in the literature, which depend on special mathematical functions such as hypergeometric functions. We verify that the arguments of the hypergeometric functions in the analytic expressions for the single and joint life an...
In this paper, we propose a general class of bivariate proportional hazard distributions, which is based on the family of asymmetric proportional hazard distributions and the bivariate Pareto copula. Distributional properties of the bivariate proportional hazard distribution are derived. We specialize the bivariate proportional hazard family of dis...
The Gompertz-Makeham model was introduced as an extension of the Gompertz model in the second half of the 19th century by the British actuary William M. Makeham. Since then, this model has been successfully used in biology, actuarial science, and demography to describe mortality patterns in numerous species (including humans), determine policies in...
In this paper, a new bivariate absolutely continuous probability distribution is introduced. The new distribution, which is called the bivariate unit-sinh-normal (BVUSHN) distribution, arises by applying a transformation to the bivariate Birnbaum–Saunders distribution (BVBS). The main properties of the new proposal are studied in detail. In additio...
This paper introduces a general class of multivariate distributions for rates and proportions on the basis of the multivariate elliptical distribution. We derive various general properties of this multivariate distribution. The model parameters are estimated using the maximum likelihood estimation method. In particular, we have considered parameter...
The discrete Bell distribution and its associated regression model were introduced recently in the statistical literature. The Bell distribution has proved to be a useful alternative to the traditional Poisson distribution, mainly to deal with overdispersion. Likelihood‐based inference on the Bell regression parameters relies on asymptotic assumpti...
The Bell distribution was introduced recently in the statistical literature. This distribution can be very similar to the Poisson distribution, and so it is quite important to provide procedures to discriminate these models. In this paper, we consider the Vuong test procedure and the Akaike information criterion to do that. Monte Carlo simulation e...
In this paper, we present a new parametric class of distributions based on the log-alpha-power distribution, which contains the well-known log-normal distribution as a special case. This new family is useful to deal with unimodal as well as bimodal data with asymmetry and kurtosis coefficients ranging far from that expected based on the log-normal...
The two-parameter Bell–Touchard distribution corresponds to a quite flexible yet tractable parametric family of discrete distributions, which arises prominently as an empirical model for count data. In this paper, we introduce a novel parametric regression model for count response variables on the basis of the mean-parameterized Bell–Touchard distr...
In this paper we introduce a multivariate family of distributions for multivariate count data with excess zeros, which is a multivariate extension of the univariate zero-inflated Bell distribution. We derive various general properties of this multivariate distribution. In particular, the marginal distributions are univariate zero-inflated Bell dist...
The univariate Birnbaum-Saunders distribution is quite useful for modeling lifetime data, reliability problems, and times to failure for materials subject to fatigue. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature. In this paper, based on the multivariate power-normal distributi...
Naradajah and Pal (Bull Braz Math Soc New Ser 39(1):45–60, 2008) derived explicit closed-form expressions for moments of order statistics from the gamma and generalized gamma distributions. However, the closed-form expressions provided by these authors are not correct and hence cannot be used to compute the moments of order statistics. We provide,...
We introduce a family of distributions with bounded support for continuous rates or proportions when the data contain zeros or ones. On the basis of this class of distributions, we propose a novel class of regression models which is useful for modelling fractional data observed on [0, 1) or (0, 1]. The response variable of the new class of regressi...
On the basis of an interesting and tractable family of distributions, which is useful to deal with asymmetry together with heavy tails, we introduce a novel parametric regression model that is quite simple and may be very useful to model many types of real data which occurs frequently in practice. The unknown parameters are estimated using the maxi...
The censored exponential regression model is commonly used for modeling lifetime data. In this paper, we derive a simple matrix formula for the second-order covariance matrix of the maximum likelihood estimators in this class of regression models. The general matrix formula covers many types of censoring commonly encountered in practice. Also, the...
The likelihood ratio, Wald, score and gradient test statistics can result in misleading conclusions when the assumed parametric model to the data at hand is not correctly specified. To overcome this issue, robust versions of these test statistics have been proposed in the statistic literature under model misspecification. In this paper, we address...
A closed-form expression for the remaining life expectancy based on the gamma-Gompertz model has been derived recently in the literature. However, the closed-form expression available to users is not correct. We provide, therefore, a valid and correct expression for the life expectancy at age x by using elementary calculus. We also consider a compa...
The one-parameter Bell family of distributions, introduced by Castellares et al. (Appl Math Model 56:172–185, 2018), is useful for modeling count data. This paper proposes and studies a goodness-of-fit test for this distribution, which is consistent against fixed alternatives. The finite sample performance of the proposed test is investigated by me...
On the basis of a two-parameter heavy-tailed distribution, we introduce a novel parametric quantile regression model for limited range response variables, which can be very useful in modeling bounded response variables at different levels (quantiles) in the presence of atypical observations. We consider a frequentist approach to perform inferences,...
The Student‐ t distribution has proved to be a useful alternative to the traditional normal distribution, mainly to deal with heavy tails and when robust estimation is desired. We consider the multivariate Student‐ t regression model and derive the nonnull asymptotic expansions (under a sequence of Pitman alternatives) of the distribution functions...
In asymptotic theory, the gradient test proposed by Terrell is a recent likelihood-based hypothesis testing approach which can be considered as an alternative to the well-established trinity of likelihood ratio, Rao score, and Wald tests. The gradient test has not yet entered into the mainstream of applied statistics. This is particularly true for...
The univariate power-normal distribution is quite useful for modeling many types of real data. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature, mainly skewed multivariate extensions that can be bimodal, for example. In this paper, based on the univariate power-normal distribution...
This paper deals with the issue of testing hypotheses in the censored exponential regression model in small and moderate-sized samples. We focus on four tests, namely the Wald, likelihood ratio, score, and gradient tests. These tests rely on asymptotic results and are unreliable when the sample size is not large enough to guarantee a good agreement...
Abd El-Bar 2018, ‘An extended Gompertz-Makeham distribution with application to lifetime data’, Communication in Statistics – Simulation and Computation, 47, 2454–2475) introduced a four-parameter extension of the Gompertz-Makeham distribution, and derived some statistical and reliability measures like moments, moment generating function, condition...
The likelihood ratio test statistic provides the basis for testing inference on the regression parameters in the class of multivariate Dirichlet regression models, which is very useful in modeling multivariate positive observations summing to one. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approxima...
By starting from the one-parameter Bell distribution proposed recently in the statistic literature, we introduce the zero-inflated Bell family of distributions. Additionally, on the basis of the proposed zero-inflated distribution, a novel zero-inflated regression model is proposed, which is quite simple and may be an interesting alternative to usu...
In this paper we consider the multivariate Dirichlet regression model proposed by Melo et al. (2009 Melo, T. F. N., K. L. P. Vasconcellos, and A. J. Lemonte. 2009. Some restriction tests in a new class of regression models for proportions. Computational Statistics and Data Analysis 53(12):3972–9. doi:10.1016/j.csda.2009.06.005.[Crossref], [Web of S...
In this paper we introduce a new two-parameter discrete distribution which may be useful for modeling count data. Additionally, the probability mass function is very simple and it may have a zero vertex. We show that the new discrete distribution is a particular solution of a multiple Poisson process, and that it is infinitely divisible. Additional...
We consider the generalized extended exponential-Weibull distribution, which can be very useful for modeling non-monotonic failure rate function, and provide a detailed study of its structural properties. This model includes at least thirteen sub-models and some of them are very known such as the Weibull, generalized Weibull, exponential-Weibull, a...
This paper introduces a new lifetime distribution to describe and analyze monotone, upside-down bathtub, bathtub-shaped and modified bathtub-shaped failure rates. An important property of the new distribution is that it can have a bathtub-shaped failure rate function with a long flat region, which may be very useful in reliability contexts. Some st...
The three-parameter generalized Gompertz distribution was introduced recently in the statistic literature as an extension of the well-known two-parameter Gompertz distribution. In addition, a closed-form expression for its moments is derived. However, we verify that this expression cannot be used for computing the moments, since the power series ex...
We address the issue of performing testing inference in the class of zero-inflated power series models. These models provide a straightforward way of modelling count data and have been widely used in practical situations. The likelihood ratio, Wald and score statistics provide the basis for testing the parameter of inflation of zeros in this class...
The cure fraction models are useful to model lifetime data with long-term survivors. In this paper, we introduce a flexible cure rate survival model where the model parameters are related to covariates in different regression structures. The regression model allows to model jointly the location, scale and shape effects. The maximum likelihood metho...
We develop nearly unbiased maximum likelihood estimators for a new class of asymmetric link functions proposed recently in the statistic literature by Lemonte and Bazán (TEST 27, 597–617 2018). These authors have introduced a broad class of parametric link functions in binary regression that contains as special cases both symmetric as well as asymm...
The paper by Johnson [Systems of frequency curves generated by the methods of translation, Biometrika 36 (2014), pp. 149–176] has introduced a very interesting univariate distribution with bounded support which is known in the statistical literature as the SB class of distributions. In this paper we generalize this class of univariate distributions...
An important challenge in the class of generalized Johnson SB regression models is to define residuals which are capable of identifying departures from the model assumptions, as well as to assess the overall goodness-of-fit of the model. On this regard, we propose a new residual for this class of models, and numerically evaluate its behaviour relat...
In this paper we define and study the one-parameter discrete Bell distribution, which has a very simple form for its probability mass function. In particular, we show that this discrete distribution is a particular solution of a multiple Poisson process. By considering the distribution studied in this article, we introduce a new regression model wh...
Binary response data arise naturally in applications. In general, the well-known logistic and probit regression models form the basis for analyzing binary data in practice. These regression models make use of symmetric link functions (logit and probit links). However, many authors have emphasized the need of asymmetric links in modeling binary resp...
We derive a general matrix Bartlett–type correction factor to the gradient statistic in the class of dispersion models. The correction improves the large–sample χ² approximation to the null distribution of the gradient statistic when the sample size is finite. We conduct Monte Carlo simulation experiments to evaluate and compare the performance of...
In this paper, a new extension for the generalized Rayleigh distribution is
introduced. The proposed model, called Marshall-Olkin extended generalized Rayleigh
distribution, arises based on the scheme introduced by Marshall and Olkin (1997).
A comprehensive account of the mathematical properties of the new distribution is provided.
The maximum like...
We introduce a new class of heteroscedastic log-exponentiated Weibull (LEW) regression models. The class of regression models can be applied to censored data and be used more effectively in survival analysis. Maximum likelihood estimation of the model parameters with censored data as well as influence diagnostics for the new regression model is inv...
In this chapter, the asymptotic expansion of the distribution function of the gradient test statistic is presented for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n−1/2, n being the sample size. Based on this asymptotic expansion, we perform local power comparisons among the gra...
In this chapter, we present a gradient statistic which is robust under model misspecification, that is, it can be used to test hypotheses without the knowledge of the true random mechanisms that underlie the data. The asymptotic distribution of the robust gradient statistic under the null hypothesis is also presented. We consider some examples and...
In this chapter, the asymptotic expansion for the null distribution function of the gradient statistic for testing composite null hypotheses in the presence of nuisance parameters is presented. Using this expansion, a Bartlett-type corrected gradient statistic with χ2 distribution up to an error of order O(n−3/2) under the null hypothesis is constr...
In this chapter, we introduce the new likelihood-based test statistic named as the gradient statistic. The test that uses the gradient statistic is a newly large-sample test which was introduced in the statistic literature by George R. Terrell. The gradient statistic is very simple to be computed and it can be an interesting alternative to the clas...
Starting from the robust Wald- and score-type tests, we construct a new robust test in general parametric models based on general M-estimators, so-called robust gradient-type test. The asymptotic properties of the robust gradient-type test statistic under the null hypothesis and under a sequence of contiguous alternatives are derived. The local sta...
We propose a new two-parameter continuous model called the extended arcsine distribution restricted to the unit interval. It is a very competitive model to the beta and Kumaraswamy distributions for modeling percentages, rates, fractions and proportions. We provide a mathematical treatment of the new distribution including explicit expressions for...
We address the issue of performing testing inference in Birnbaum-Saunders nonlinear regression models when the sample size is small. The likelihood ratio, Wald and score statistics provide the basis for testing inference on the parameters in this class of models. We focus on the small-sample case, where the reference chi-squared distribution gives...
We introduce a new three-parameter lifetime model called the odd Birnbaum–Saunders distribution. We construct an extended regression model based on the logarithm of the new distribution, which can be applied to censored data and be more effectively in analysing real data. Maximum likelihood estimation of the model parameters of the new regression m...
A general method of introducing a new parameter to a well-established continuous baseline cumulative function G to obtain more flexible distributions was proposed by Marshall and Olkin (1997). This new family is known as Marshall–Olkin extended G family of distributions. In this article, we characterize this family as mixtures of the distributions...
We show that the Fisher information matrix of the Birnbaum–Saunders distribution can present numerical problems for some values of the shape parameter. To overcome this problem, we provide a simple analytical approximation which works very well.
We propose a new and simple representation for the gamma dual G probability density function, recently introduced in the statistical literature, as an absolutely convergent power series of the survival function of the baseline G distribution. Additionally, the three-parameter gamma dual Weibull model is studied. Some similarities and differences be...
We address the issue of performing testing inference in Birnbaum-Saunders nonlinear regression models when the sample size is small. The likelihood ratio, Wald and score statistics provide the basis for testing inference on the parameters in this class of models. We focus on the small-sample case, where the reference chi-squared distribution gives...
A three-parameter extension of the exponential distribution is introduced and studied in this paper. The new distribution is quite flexible and can be used effectively in modelling survival data, reliability problems, fatigue life studies and hydrological data. It can have constant, decreasing, increasing, upside-down bathtub (unimodal), bathtub-sh...
The Gradient Test: Another Likelihood-Based Test presents the latest on the gradient test, a large-sample test that was introduced in statistics literature by George R. Terrell in 2002. The test has been studied by several authors, is simply computed, and can be an interesting alternative to the classical large-sample tests, namely, the likelihood...
In this paper, a new extension for the generalized Rayleigh distribution is
introduced. The proposed model, called Marshall-Olkin extended generalized Rayleigh
distribution, arises based on the scheme introduced by Marshall and Olkin (1997).
A comprehensive account of the mathematical properties of the new distribution is provided.
The maximum like...
By starting from the Johnson SB distribution pioneered by Johnson (), we propose a broad class of distributions with bounded support on the basis of the symmetric family of distributions. The new class of distributions provides a rich source of alternative distributions for analyzing univariate bounded data. A comprehensive account of the mathemati...
We propose a robust likelihood approach for the Birnbaum-Saunders regression model under model misspecification, which provides full likelihood inferences about regression parameters without knowing the true random mechanisms underlying the data. Monte Carlo simulation experiments and analysis of real data sets are carried out to illustrate the eff...
In this paper we introduce a new three-parameter exponential-type distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have constant, decreasing, increasing, upside-down bathtub and bathtub-shaped hazard rate functions. It also generalizes some well-known distrib...
A new continuous distribution, so-called the beta log-logistic distribution, that extends the log-logistic distribution and some other distributions is proposed and studied. The new model is quite flexible to analyze positive data. Various structural properties of the new distribution are derived, including explicit expressions for the moments, mea...
The univariate fatigue life distribution proposed by Birnbaum and Saunders [A new family of life distributions. J Appl Probab. 1969;6:319–327] has been used quite effectively to model times to failure for materials subject to fatigue and for modelling lifetime data and reliability problems. In this article, we introduce a Birnbaum–Saunders (BS) dis...
A new distribution called the exponentiated generalized Birnbaum-Saunders distribution is proposed and studied. The new distribution is quite flexible to model survival data, reliability problems, fatigue life studies and hydrological data. It can have decreasing, increasing, upside-down bathtub, bathtub-shaped, increasing-decreasing-increasing and...
The local powers of some tests under the presence of a parameter vector, \(\varvec{\omega }\) say, that is orthogonal to the remaining parameters are studied in this paper. We show that some of the coefficients that define the local powers of the tests remain unchanged regardless of whether \(\varvec{\omega }\) is known or needs to be estimated, wh...
In this article, we consider the class of censored exponential regression models which is very useful for modeling lifetime data. Under a sequence of Pitman alternatives, the asymptotic expansions up to order n − 1/2 of the non null distribution functions of the likelihood ratio, Wald, Rao score, and gradient statistics are derive in this class of...
A new continuous distribution, so-called the beta log-logistic distribution, that extends the log-logistic distribution and some other distributions is proposed and studied. The new model is quite flexible to analyze positive data. Various structural properties of the new distribution are derived, including explicit expressions for the moments, mea...
We derive explicit expressions for the moments, incomplete moments, quantile function and generating function of the additive Weibull model pioneered by Xie and Lai (199518.
Xie, M., Lai, C.D. (1995). Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliab. Eng. Syst. Safety 52:87–93.[CrossRef], [Web o...
A new method for generating new classes of distributions based on the probability-generating function is presented in Aly and Benkherouf [A new family of distributions based on probability generating functions. Sankhya B. 2011;73:70-80]. In particular, they focused their interest to the so-called Harris extended family of distributions. In this pap...
We propose a new and simple representation for the probability density function of the gamma-G family of distributions as an absolutely convergent power series of the cumulative function of the baseline G distribution. Additionally, the special case the so-called gamma exponentiated Weibull model is introduced and studied in details.
Marshall and Olkin (1997) introduced a general method for obtaining more flexible distributions by adding a new parameter to an existing one, called the Marshall–Olkin family of distributions. In this article, we provide a comprehensive treatment of general mathematical and statistical properties of this family of distributions. Moreover, we propos...
We formulate a new cure rate survival model by assuming that the number of competing causes of the event of interest has the Poisson distribution, and the time to this event has the generalized linear failure rate distribution. A new distribution to analyze lifetime data is defined from the proposed cure rate model, and its quantile function as wel...
In this paper, we introduce a bivariate Kumaraswamy (BVK) distribution whose marginals are Kumaraswamy distributions. The cumulative distribution function of this bivariate model has absolutely continuous and singular parts. Representations for the cumulative and density functions are presented and properties such as marginal and conditional distri...
We address the issue of performing testing inference in generalized linear
models when the sample size is small. This class of models provides a
straightforward way of modeling normal and non-normal data and has been widely
used in several practical situations. The likelihood ratio, Wald and score
statistics, and the recently proposed gradient stat...
A new class of extended Birnbaum–Saunders regression models is introduced. It can be applied to censored data and be used more effectively in survival analysis and fatigue life studies. Maximum likelihood estimation of the model parameters with censored data as well as influence diagnostics for the new regression model are investigated. The normal...
A new three-parameter exponential-type family of distributions which can be used in modeling survival data, reliability problems and fatigue life studies is introduced. Its failure rate function can be constant, decreasing, increasing, upside-down bathtub or bathtub-shaped depending on its parameters. It includes as special sub-models the exponenti...
A general method of introducing a new parameter to a well-established continuous baseline cumulative function G to obtain more flexible distributions was proposed by Marshall and Olkin (1997)25.
Marshall, A.W., Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families...
In this paper, a new extension for the Birnbaum–Saunders distribution, which has been applied to the modeling of fatigue failure times and reliability studies, is introduced. The proposed model, called the Marshall–Olkin extended Birnbaum–Saunders distribution, arises based on the scheme introduced by Marshall and Olkin [Biometrika 84 (1997) 641–65...
In this paper, we propose a new three-parameter model called the exponential-Weibull distribution, which includes as special models some widely known lifetime distributions. Some mathematical properties of the proposed distribution are investigated. We derive four explicit expressions for the generalized ordinary moments and a general formula for t...
Marshall and Olkin (1997) introduced an interesting method of adding a parameter to a well-established distribution. However, they did not investigate general mathematical properties of their family of distributions. We provide for this family of distributions general expansions for the density function, explicit expressions for the moments and mom...
The paper by Kumaraswamy (Journal of Hydrology 46 (1980) 79–88) introduced a probability distribution for double bounded random processes which has considerable attention in hydrology and related areas. Based on this distribution, we propose a generalization of the Kumaraswamy distribution refereed to as the exponentiated Kumaraswamy distribution....
