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Papers by Victor Leiva

Research paper thumbnail of M-PROCEDURES IN THE GENERAL MULTIVARIATE NONLINEAR REGRESSION MODEL

Pakistan Journal of Statistics, 2010

In the multivariate nonlinear regression model, parameter estimators and test statistics based on... more In the multivariate nonlinear regression model, parameter estimators and test statistics based on least squares and maximum likelihood methods are usually nonrobust. For this type of models, we introduce M-estimators and M-tests, which are robust to departures from normality. In addition, we study the asymptotic properties and consider a computational algorithm for these estimators.

Research paper thumbnail of A unified mixture model based on the inverse Gaussian distribution

Pakistan Journal of Statistics, 2010

... In the nor-mal case, Lange et al. (1989), Lange and Sinheimer (1993) and Lucas (1997) propose... more ... In the nor-mal case, Lange et al. (1989), Lange and Sinheimer (1993) and Lucas (1997) proposed to use models with greater kurtosis than the normal model in order to solve this problem and obtain qualitatively robust estimators. ... (2009) Víctor Leiva et al. 447 Page 4. ...

Research paper thumbnail of NEW CONTROL CHARTS BASED ON THE BIRNBAUM-SAUNDERS DISTRIBUTION AND THEIR IMPLEMENTATION

Revista Colombiana De Estadistica, Apr 18, 2012

The Birnbaum-Saunders (BS) model is a life distribution with interesting properties and applicati... more The Birnbaum-Saunders (BS) model is a life distribution with interesting properties and applications in several fields. This has transformed the BS model in an important research focus in recent decades. However, the sum of BS (BSsum) independent random variables does not follow a BS distribution. By means of the BSsum distribution, we can monitor the lifetime of products subject to failures using a quality control chart. Classic procedures for control charts assume normality in the distribution of the data. Nevertheless, one of the main characteristics of the lifetimes is that them generally follow asymmetric distributions. Therefore, if we want to monitor these lifetimes, we must consider control charts for asymmetric distributions, such as it is the case of the BS distribution. The monitoring of the lifetimes is carried out generally by the accumulated lifetime or the lifetime average until than a number of failures occurs. Thus, by using the BSsum distribution, we develop, implement and apply a new methodology for control charts based on the BS distribution.

Research paper thumbnail of A Robust Procedure in Nonlinear Models for Repeated Measurements

Commun Statist Theor Method, 2008

Nonlinear regression models arise when definite information is available about the form of the re... more Nonlinear regression models arise when definite information is available about the form of the relationship between the response and predictor variables. Such information might involve direct knowledge of the actual form of the true model or might be represented by a set of differential equations that the model must satisfy. We develop M-procedures for estimating parameters and testing hypotheses of

Research paper thumbnail of Special Virtual Issue of Communications in Statistics Communications in Statistics: Theory and Methods 1. A Skewed Sinh-Normal Distribution and Its Properties and Application to Air Pollution

As an important step of assessing the impact and contribution of the Communications in Statistics... more As an important step of assessing the impact and contribution of the Communications in Statistics journals, Editor-in-Chief N. Balakrishnan has identified some of the key publications from the journals which over time have found many citations and incited several other related works. We hope this virtual issue with the collection of such "high-impacting" articles will be found to be useful by the readers.

Research paper thumbnail of Modeling neural activity with cumulative damage distributions

Biological Cybernetics, 2015

Neurons transmit information as action potentials or spikes. Due to the inherent randomness of th... more Neurons transmit information as action potentials or spikes. Due to the inherent randomness of the inter-spike intervals (ISIs), probabilistic models are often used for their description. Cumulative damage (CD) distributions are a family of probabilistic models that has been widely considered for describing time-related cumulative processes. This family allows us to consider certain deterministic principles for modeling ISIs from a probabilistic viewpoint and to link its parameters to values with biological interpretation. The CD family includes the Birnbaum-Saunders and inverse Gaussian distributions, which possess distinctive properties and theoretical arguments useful for ISI description. We expand the use of CD distributions to the modeling of neural spiking behavior, mainly by testing the suitability of the Birnbaum-Saunders distribution, which has not been studied in the setting of neural activity. We validate this expansion with original experimental and simulated electrophysiological data.

Research paper thumbnail of A Skewed Sinh-Normal Distribution and Its Properties and Application to Air Pollution

Communications in Statistics-theory and Methods, 2010

In this article, we introduce a skewed version of the sinh-normal distribution and discuss some o... more In this article, we introduce a skewed version of the sinh-normal distribution and discuss some of its properties. In addition, we characterize an extension of the Birnbaum–Saunders model associated with this distribution from a probabilistic viewpoint along with a lifetime analysis based on its hazard rate. Finally, one of the proposed models is applied to air pollution data in order

Research paper thumbnail of Graphical Tools to Assess Goodness-of-Fit in Non-Location-Scale Distributions

Revista Colombiana de Estadística, 2014

Goodness-of-fit (GOF) techniques are used for assessment whether a distribution is suitable to de... more Goodness-of-fit (GOF) techniques are used for assessment whether a distribution is suitable to describe a data set or not. These techniques have been studied for distributions belonging to the location-scale family. However, one could be interested in making this assessment for distributions that do not belong to this family. We review the available GOF tests and propose graphical tools based on these tests for censored and uncensored data from non-location-scale distributions. Anderson-Darling, Cramér-von Mises, Kolmogorov-Smirnov, Kuiper, Michael and Watson GOF statistics are considered. We apply the proposed results to real-world data sets to illustrate their potential, with emphasis on some Birnbaum-Saunders distributions.

Research paper thumbnail of Successful aminolevulinic acid photodynamic therapy for recalcitrant severe hidradenitis suppurativa

Photodermatology, photoimmunology & photomedicine, 2010

Research paper thumbnail of Mixture inverse Gaussian distributions and its transformations, moments and applications

Statistics, 2009

Skewed models are important and necessary when parametric analyses are carried out on data. Mixtu... more Skewed models are important and necessary when parametric analyses are carried out on data. Mixture distributions produce widely flexible models with good statistical and probabilistic properties, and the mixture inverse Gaussian (MIG) model is one of those. Transformations of the MIG model also create new parametric distributions, which are useful in diverse situations. The aim of this paper is to

Research paper thumbnail of An extended Birnbaum–Saunders model and its application in the study of environmental quality in Santiago, Chile

Stochastic Environmental Research and Risk Assessment, 2010

In this article, we introduce, characterize and apply an extended version of the Birnbaum–Saunder... more In this article, we introduce, characterize and apply an extended version of the Birnbaum–Saunders model based on the Mudolkar–Hutson skew distribution. This model is appropriated for describing phenomena involving accumulation of some type, as is the case of environmental contamination. Specifically, we find the density, distribution function, and moments of the new model. In addition, we derive several properties and

Research paper thumbnail of A length-biased version of the Birnbaum-Saunders distribution with application in water quality

Stochastic Environmental Research and Risk Assessment, 2009

Abstract In this article, we develop a new model based on the Birnbaum-Saunders distribution that... more Abstract In this article, we develop a new model based on the Birnbaum-Saunders distribution that results to be both useful and practical for environmental sciences. The density, distribution and hazard functions, moments and properties of this new model are presented. A ...

Research paper thumbnail of A new three-parameter extension of the inverse Gaussian distribution

Statistics & Probability Letters, 2008

In this article, we introduce a new model that extends the inverse Gaussian distribution. This mo... more In this article, we introduce a new model that extends the inverse Gaussian distribution. This model is obtained when a parameter is incorporated into the logarithmic inverse Gaussian distribution producing great flexibility for fitting non-negative data. We present a comprehensive ...

Research paper thumbnail of Influence diagnostics in the tobit censored response model

Statistical Methods & Applications, 2010

In this article, we develop influence diagnostic tools for the tobit model. Specifically, we disc... more In this article, we develop influence diagnostic tools for the tobit model. Specifically, we discuss global influence methods based on the Cook distance and residuals with envelopes, and total and conformal local influence techniques. In order to analyze the sensitivity of the maximum likelihood estimators of the parameters of the model to small perturbations on the assumptions of the model and/or data, we consider several perturbation schemes, such as case-weight and response perturbations. Finally, we illustrate the developed methodology by means of a real data set.

Research paper thumbnail of Un nuevo modelo de vida Birnbaum Saunders con daño acumulativo dependiente

La distribución Birnbaum Saunders de dos parámetros fue derivada en 1969 a partir de un modelo de... more La distribución Birnbaum Saunders de dos parámetros fue derivada en 1969 a partir de un modelo de vida por fatiga cuando un especimen está expuesto a estrés cíclico y tensión, y la última falla del especimen se debe al crecimiento de la grieta dominante en el material. La derivación de este modelo, se basa en supuestos restrictivos para el proceso de fatiga de material y que en muchas situaciones experimentales no son adecuados. Presentamos en este trabajo el relajo del supuesto de independencia para el tamaño de la grieta, considerando la secuencia del tamaño de ésta como un proceso estocástico a largo plazo. Cuando esta modificación se incorpora a la derivación, el modelo resultante es una nueva generalización de tres parámetros a la distribución Birnbaum Saunders original. También presentamos algunas propiedades de este modelo e ideas para futuras líneas de investigación.

Research paper thumbnail of A new class of inverse Gaussian type distributions

Metrika, 2008

The elliptical laws are a class of symmetrical probability models that include both lighter and h... more The elliptical laws are a class of symmetrical probability models that include both lighter and heavier tailed distributions. These models may adapt well to the data, even when outliers exist and have other good theoretical properties and application perspectives. In this article, we present a new class of models, which is generated from symmetrical distributions in R and generalize the well known inverse Gaussian distribution. Specifically, the density, distribution function, properties, transformations and moments of this new model are obtained. Also, a graphical analysis of the density is provided. Furthermore, we estimate parameters, propose asymptotic inference and discuss influence diagnostics by using likelihood methods for the new distribution. In particular, we show that the maximum likelihood estimates parameters of the new model under the t kernel are down-weighted for the outliers. Thus, smaller weights are attributed to outlying observations, which produce robust parameter estimates. Finally, an illustrative example with real data shows that the new distribution fits better to the data than some other well known probabilistic models.

Research paper thumbnail of Two New Mixture Models Related to the Inverse Gaussian Distribution

Methodology and Computing in Applied Probability, 2010

This article presents a new family of logarithmic distributions to be called the sinh mixture inv... more This article presents a new family of logarithmic distributions to be called the sinh mixture inverse Gaussian model and its associated life distribution referred as the extended mixture inverse Gaussian model. Specifically, the density, distribution function, and moments are developed for the sinh mixture inverse Gaussian distribution. Next, the extended mixture inverse Gaussian distribution is characterized. A graphical analysis of the densities of the new models is also provided. In addition, a lifetime analysis is presented for the extended mixture inverse Gaussian distribution. Finally, an example with a real data set is given to illustrate the methodology, which indicates that the new models result in a better fit to the data than some other wellknown distributions.

Research paper thumbnail of A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Lifetime Data Analysis, 2008

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability an... more Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

Research paper thumbnail of Erratum to “A new family of life distributions based on the elliptically contoured distributions”

Journal of Statistical Planning and Inference, 2007

P. 446 line 10. In Equation 1, the function (·) must be defined from R + to R rather than from R ... more P. 446 line 10. In Equation 1, the function (·) must be defined from R + to R rather than from R to R. P. 446 line 20. In Remark 1 part (i), the parameter r should be equal to for the statement to be valid. P. 446 line 25. In Remark 1 part (iii), the special case distribution has mean 0 and variance 2 . However, for n 3, E(X n ) does not exist (it diverges). P. 446 line 29. In Remark 1 part (v), the parameters q = 0 and r = / √ 2 should be changed to q = 1/2 and r = for the statement to be valid. P. 447 line 12. In , the notation SC( , 2 ) for the special case distribution must be changed to SC( = 0, 2 ).

Research paper thumbnail of On some mixture models based on the Birnbaum–Saunders distribution and associated inference

Journal of Statistical Planning and Inference, 2011

In this paper, we consider three different mixture models based on the Birnbaum-Saunders (BS) dis... more In this paper, we consider three different mixture models based on the Birnbaum-Saunders (BS) distribution, viz., (1) mixture of two different BS distributions, (2) mixture of a BS distribution and a length-biased version of another BS distribution, and (3) mixture of the BS distribution and its length-biased version. For all these models, we study their structural properties as well as the shape of their density and hazard rate functions. For the maximum likelihood estimation of the model parameters, we utilize the EM algorithm, which is described and implemented. For the purpose of illustration, we analyze two data sets related to enzyme and depressive condition problems. In the case of enzyme data, it is shown that Model 1 provides the best fit, while for the depressive condition data, it is shown all three models fit well with Model 3 providing the best fit.

Research paper thumbnail of M-PROCEDURES IN THE GENERAL MULTIVARIATE NONLINEAR REGRESSION MODEL

Pakistan Journal of Statistics, 2010

In the multivariate nonlinear regression model, parameter estimators and test statistics based on... more In the multivariate nonlinear regression model, parameter estimators and test statistics based on least squares and maximum likelihood methods are usually nonrobust. For this type of models, we introduce M-estimators and M-tests, which are robust to departures from normality. In addition, we study the asymptotic properties and consider a computational algorithm for these estimators.

Research paper thumbnail of A unified mixture model based on the inverse Gaussian distribution

Pakistan Journal of Statistics, 2010

... In the nor-mal case, Lange et al. (1989), Lange and Sinheimer (1993) and Lucas (1997) propose... more ... In the nor-mal case, Lange et al. (1989), Lange and Sinheimer (1993) and Lucas (1997) proposed to use models with greater kurtosis than the normal model in order to solve this problem and obtain qualitatively robust estimators. ... (2009) Víctor Leiva et al. 447 Page 4. ...

Research paper thumbnail of NEW CONTROL CHARTS BASED ON THE BIRNBAUM-SAUNDERS DISTRIBUTION AND THEIR IMPLEMENTATION

Revista Colombiana De Estadistica, Apr 18, 2012

The Birnbaum-Saunders (BS) model is a life distribution with interesting properties and applicati... more The Birnbaum-Saunders (BS) model is a life distribution with interesting properties and applications in several fields. This has transformed the BS model in an important research focus in recent decades. However, the sum of BS (BSsum) independent random variables does not follow a BS distribution. By means of the BSsum distribution, we can monitor the lifetime of products subject to failures using a quality control chart. Classic procedures for control charts assume normality in the distribution of the data. Nevertheless, one of the main characteristics of the lifetimes is that them generally follow asymmetric distributions. Therefore, if we want to monitor these lifetimes, we must consider control charts for asymmetric distributions, such as it is the case of the BS distribution. The monitoring of the lifetimes is carried out generally by the accumulated lifetime or the lifetime average until than a number of failures occurs. Thus, by using the BSsum distribution, we develop, implement and apply a new methodology for control charts based on the BS distribution.

Research paper thumbnail of A Robust Procedure in Nonlinear Models for Repeated Measurements

Commun Statist Theor Method, 2008

Nonlinear regression models arise when definite information is available about the form of the re... more Nonlinear regression models arise when definite information is available about the form of the relationship between the response and predictor variables. Such information might involve direct knowledge of the actual form of the true model or might be represented by a set of differential equations that the model must satisfy. We develop M-procedures for estimating parameters and testing hypotheses of

Research paper thumbnail of Special Virtual Issue of Communications in Statistics Communications in Statistics: Theory and Methods 1. A Skewed Sinh-Normal Distribution and Its Properties and Application to Air Pollution

As an important step of assessing the impact and contribution of the Communications in Statistics... more As an important step of assessing the impact and contribution of the Communications in Statistics journals, Editor-in-Chief N. Balakrishnan has identified some of the key publications from the journals which over time have found many citations and incited several other related works. We hope this virtual issue with the collection of such "high-impacting" articles will be found to be useful by the readers.

Research paper thumbnail of Modeling neural activity with cumulative damage distributions

Biological Cybernetics, 2015

Neurons transmit information as action potentials or spikes. Due to the inherent randomness of th... more Neurons transmit information as action potentials or spikes. Due to the inherent randomness of the inter-spike intervals (ISIs), probabilistic models are often used for their description. Cumulative damage (CD) distributions are a family of probabilistic models that has been widely considered for describing time-related cumulative processes. This family allows us to consider certain deterministic principles for modeling ISIs from a probabilistic viewpoint and to link its parameters to values with biological interpretation. The CD family includes the Birnbaum-Saunders and inverse Gaussian distributions, which possess distinctive properties and theoretical arguments useful for ISI description. We expand the use of CD distributions to the modeling of neural spiking behavior, mainly by testing the suitability of the Birnbaum-Saunders distribution, which has not been studied in the setting of neural activity. We validate this expansion with original experimental and simulated electrophysiological data.

Research paper thumbnail of A Skewed Sinh-Normal Distribution and Its Properties and Application to Air Pollution

Communications in Statistics-theory and Methods, 2010

In this article, we introduce a skewed version of the sinh-normal distribution and discuss some o... more In this article, we introduce a skewed version of the sinh-normal distribution and discuss some of its properties. In addition, we characterize an extension of the Birnbaum–Saunders model associated with this distribution from a probabilistic viewpoint along with a lifetime analysis based on its hazard rate. Finally, one of the proposed models is applied to air pollution data in order

Research paper thumbnail of Graphical Tools to Assess Goodness-of-Fit in Non-Location-Scale Distributions

Revista Colombiana de Estadística, 2014

Goodness-of-fit (GOF) techniques are used for assessment whether a distribution is suitable to de... more Goodness-of-fit (GOF) techniques are used for assessment whether a distribution is suitable to describe a data set or not. These techniques have been studied for distributions belonging to the location-scale family. However, one could be interested in making this assessment for distributions that do not belong to this family. We review the available GOF tests and propose graphical tools based on these tests for censored and uncensored data from non-location-scale distributions. Anderson-Darling, Cramér-von Mises, Kolmogorov-Smirnov, Kuiper, Michael and Watson GOF statistics are considered. We apply the proposed results to real-world data sets to illustrate their potential, with emphasis on some Birnbaum-Saunders distributions.

Research paper thumbnail of Successful aminolevulinic acid photodynamic therapy for recalcitrant severe hidradenitis suppurativa

Photodermatology, photoimmunology & photomedicine, 2010

Research paper thumbnail of Mixture inverse Gaussian distributions and its transformations, moments and applications

Statistics, 2009

Skewed models are important and necessary when parametric analyses are carried out on data. Mixtu... more Skewed models are important and necessary when parametric analyses are carried out on data. Mixture distributions produce widely flexible models with good statistical and probabilistic properties, and the mixture inverse Gaussian (MIG) model is one of those. Transformations of the MIG model also create new parametric distributions, which are useful in diverse situations. The aim of this paper is to

Research paper thumbnail of An extended Birnbaum–Saunders model and its application in the study of environmental quality in Santiago, Chile

Stochastic Environmental Research and Risk Assessment, 2010

In this article, we introduce, characterize and apply an extended version of the Birnbaum–Saunder... more In this article, we introduce, characterize and apply an extended version of the Birnbaum–Saunders model based on the Mudolkar–Hutson skew distribution. This model is appropriated for describing phenomena involving accumulation of some type, as is the case of environmental contamination. Specifically, we find the density, distribution function, and moments of the new model. In addition, we derive several properties and

Research paper thumbnail of A length-biased version of the Birnbaum-Saunders distribution with application in water quality

Stochastic Environmental Research and Risk Assessment, 2009

Abstract In this article, we develop a new model based on the Birnbaum-Saunders distribution that... more Abstract In this article, we develop a new model based on the Birnbaum-Saunders distribution that results to be both useful and practical for environmental sciences. The density, distribution and hazard functions, moments and properties of this new model are presented. A ...

Research paper thumbnail of A new three-parameter extension of the inverse Gaussian distribution

Statistics & Probability Letters, 2008

In this article, we introduce a new model that extends the inverse Gaussian distribution. This mo... more In this article, we introduce a new model that extends the inverse Gaussian distribution. This model is obtained when a parameter is incorporated into the logarithmic inverse Gaussian distribution producing great flexibility for fitting non-negative data. We present a comprehensive ...

Research paper thumbnail of Influence diagnostics in the tobit censored response model

Statistical Methods & Applications, 2010

In this article, we develop influence diagnostic tools for the tobit model. Specifically, we disc... more In this article, we develop influence diagnostic tools for the tobit model. Specifically, we discuss global influence methods based on the Cook distance and residuals with envelopes, and total and conformal local influence techniques. In order to analyze the sensitivity of the maximum likelihood estimators of the parameters of the model to small perturbations on the assumptions of the model and/or data, we consider several perturbation schemes, such as case-weight and response perturbations. Finally, we illustrate the developed methodology by means of a real data set.

Research paper thumbnail of Un nuevo modelo de vida Birnbaum Saunders con daño acumulativo dependiente

La distribución Birnbaum Saunders de dos parámetros fue derivada en 1969 a partir de un modelo de... more La distribución Birnbaum Saunders de dos parámetros fue derivada en 1969 a partir de un modelo de vida por fatiga cuando un especimen está expuesto a estrés cíclico y tensión, y la última falla del especimen se debe al crecimiento de la grieta dominante en el material. La derivación de este modelo, se basa en supuestos restrictivos para el proceso de fatiga de material y que en muchas situaciones experimentales no son adecuados. Presentamos en este trabajo el relajo del supuesto de independencia para el tamaño de la grieta, considerando la secuencia del tamaño de ésta como un proceso estocástico a largo plazo. Cuando esta modificación se incorpora a la derivación, el modelo resultante es una nueva generalización de tres parámetros a la distribución Birnbaum Saunders original. También presentamos algunas propiedades de este modelo e ideas para futuras líneas de investigación.

Research paper thumbnail of A new class of inverse Gaussian type distributions

Metrika, 2008

The elliptical laws are a class of symmetrical probability models that include both lighter and h... more The elliptical laws are a class of symmetrical probability models that include both lighter and heavier tailed distributions. These models may adapt well to the data, even when outliers exist and have other good theoretical properties and application perspectives. In this article, we present a new class of models, which is generated from symmetrical distributions in R and generalize the well known inverse Gaussian distribution. Specifically, the density, distribution function, properties, transformations and moments of this new model are obtained. Also, a graphical analysis of the density is provided. Furthermore, we estimate parameters, propose asymptotic inference and discuss influence diagnostics by using likelihood methods for the new distribution. In particular, we show that the maximum likelihood estimates parameters of the new model under the t kernel are down-weighted for the outliers. Thus, smaller weights are attributed to outlying observations, which produce robust parameter estimates. Finally, an illustrative example with real data shows that the new distribution fits better to the data than some other well known probabilistic models.

Research paper thumbnail of Two New Mixture Models Related to the Inverse Gaussian Distribution

Methodology and Computing in Applied Probability, 2010

This article presents a new family of logarithmic distributions to be called the sinh mixture inv... more This article presents a new family of logarithmic distributions to be called the sinh mixture inverse Gaussian model and its associated life distribution referred as the extended mixture inverse Gaussian model. Specifically, the density, distribution function, and moments are developed for the sinh mixture inverse Gaussian distribution. Next, the extended mixture inverse Gaussian distribution is characterized. A graphical analysis of the densities of the new models is also provided. In addition, a lifetime analysis is presented for the extended mixture inverse Gaussian distribution. Finally, an example with a real data set is given to illustrate the methodology, which indicates that the new models result in a better fit to the data than some other wellknown distributions.

Research paper thumbnail of A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Lifetime Data Analysis, 2008

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability an... more Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

Research paper thumbnail of Erratum to “A new family of life distributions based on the elliptically contoured distributions”

Journal of Statistical Planning and Inference, 2007

P. 446 line 10. In Equation 1, the function (·) must be defined from R + to R rather than from R ... more P. 446 line 10. In Equation 1, the function (·) must be defined from R + to R rather than from R to R. P. 446 line 20. In Remark 1 part (i), the parameter r should be equal to for the statement to be valid. P. 446 line 25. In Remark 1 part (iii), the special case distribution has mean 0 and variance 2 . However, for n 3, E(X n ) does not exist (it diverges). P. 446 line 29. In Remark 1 part (v), the parameters q = 0 and r = / √ 2 should be changed to q = 1/2 and r = for the statement to be valid. P. 447 line 12. In , the notation SC( , 2 ) for the special case distribution must be changed to SC( = 0, 2 ).

Research paper thumbnail of On some mixture models based on the Birnbaum–Saunders distribution and associated inference

Journal of Statistical Planning and Inference, 2011

In this paper, we consider three different mixture models based on the Birnbaum-Saunders (BS) dis... more In this paper, we consider three different mixture models based on the Birnbaum-Saunders (BS) distribution, viz., (1) mixture of two different BS distributions, (2) mixture of a BS distribution and a length-biased version of another BS distribution, and (3) mixture of the BS distribution and its length-biased version. For all these models, we study their structural properties as well as the shape of their density and hazard rate functions. For the maximum likelihood estimation of the model parameters, we utilize the EM algorithm, which is described and implemented. For the purpose of illustration, we analyze two data sets related to enzyme and depressive condition problems. In the case of enzyme data, it is shown that Model 1 provides the best fit, while for the depressive condition data, it is shown all three models fit well with Model 3 providing the best fit.