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The Fama-French model is widely used in assessing the portfolio's performance compared to market returns. In Fama-French models, all factors are time-series data. The cross-sectional data are slightly different from the time series data. A distinct problem with time-series regressions is that R-squared in time series regressions is usually very high, especially compared with typical R-squared for cross-sectional data. The high value of R-squared may cause misinterpretation that the regression model fits the observed data well, and the variance in the dependent variable is explained well by the independent variables. Thus, to do regression analysis, and overcome with the serial dependence and volatility clustering, we use standard econometrics time series models to derive sample innovations. In this study, we revisit and validate the Fama-French models in two different ways: using the factors and asset returns in the Fama-French model and considering the sample innovations in the Fama-French model instead of studying the factors. Comparing the two methods considered in this study, we suggest the Fama-French model should be considered with heavy tail distributions as the tail behavior is relevant in Fama-French models, including financial data, and the QQ plot does not validate that the choice of the normal distribution as the theoretical distribution for the noise in the model.

Recently, a generalized test approach is proposed by Sadooghi-alvandi et al. (2016) and a fiducial approach is proposed by Xu and Li (2018) to test the equality of coefficients in several regression models with unequal variances. In this paper, it is shown that the considered quantities in these approaches are identically distributed and therefore, these approaches are same. Also, this result satisfies for the one-way ANOVA problem.

This paper utilizes the modified signed log-likelihood ratio method for the problem of inference about the common coefficient of variation in several independent normal populations. This method is applicable for both the problem of hypothesis testing and constructing a confidence interval for this parameter. Simulation studies show that the coverage probability of this proposed approach is close to the confidence coefficient. Also, its expected length is smaller than expected lengths of other competing approaches. In fact, the proposed approach is very satisfactory regardless of the number of populations and the different values of the common coefficient of variation even for very small sample size. Finally, we illustrate the proposed method using two real data sets.

The exponential distribution is applied in a very wide variety of statistical procedures. Among the most prominent applications are those in the field of life testing and reliability theory. When there are two record samples available for estimating the scale parameter, a preliminary test is usually used to determine whether to pool the samples or use the individual sample. In this paper, the preliminary test estimator and shrinkage estimator are studied. The optimum level of significance for preliminary test estimation and the optimum values of shrinkage coefficient are obtained based on minimax regret criterion under the weighted square error loss function., Comment: Accepted for publication in Journal of Statistical Research of Iran

In this paper, we introduce a new extension of the generalized linear failure rate distributions. It includes some well-known lifetime distributions such as extension of generalized exponential and generalized linear failure rate distributions as special sub-models. In addition, it can have a constant, decreasing, increasing, upside-down bathtub (unimodal), and bathtub-shaped hazard rate function depending on its parameters. We provide some of its statistical properties such as moments, quantiles, skewness, kurtosis, hazard rate function, and reversible hazard rate function. The maximum likelihood estimation of the parameters is also discussed. At the end, a real data set is given to illustrate the usefulness of this new distribution in analyzing lifetime data.

In this paper, we introduce the Gompertz power series class of distributions which is obtained by compounding Gompertz and power series distributions. This distribution contains several lifetime models such as Gompertz-geometric, Gompertz-Poisson, Gompertz-binomial, and Gompertz-logarithmic distributions as special cases. Sub-models of the GPS distribution are studied in details. The hazard rate function of the GPS distribution can be increasing, decreasing, and bathtub-shaped. We obtain several properties of the GPS distribution such as its probability density function, and failure rate function, Shannon entropy, mean residual life function, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented, and simulation studies are performed for evaluation of this estimation for complete data, and the MLE of parameters for censored data. At the end, a real example is given.

In this paper, we introduce the generalized Gompertz-power series class of distributions which is obtained by compounding generalized Gompertz and power series distributions. This compounding procedure follows same way that was previously carried out by Silva et al. (2013) and Barreto-Souza et al. (2011) in introducing the compound class of extended Weibull-power series distribution and the Weibull-geometric distribution, respectively. This distribution contains several lifetime models such as generalized Gompertz, generalized Gompertz-geometric, generalized Gompertz-poisson, generalized Gompertz-binomial distribution, and generalized Gompertz-logarithmic distribution as special cases. The hazard rate function of the new class of distributions can be increasing, decreasing and bathtub-shaped. We obtain several properties of this distribution such as its probability density function, Shannon entropy, its mean residual life and failure rate functions, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented, and sub-models of the distribution are studied in details., Comment: Accepted for publication

The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and alimentary science, ect. Comparison of means of several log-normal populations always has been in focus of researchers, but the test statistic are not easy to derive or extremely complicated for this comparisons. In this paper, the different methods exist for this testing that we can point out F-test, likelihood ratio test, generalized p-value approach and computational approach test. In this line with help of simulation studies, in this methods we compare and evaluate size and power test.

Recently it has been observed that the bivariate generalized linear failure rate distribution can be used quite effectively to analyze lifetime data in two dimensions. This paper introduces a more general class of bivariate distributions. We refer to this new class of distributions as bivariate generalized linear failure rate power series model. This new class of bivariate distributions contains several lifetime models such as: generalized linear failure rate-power series, bivariate generalized linear failure rate and bivariate generalized linear failure rate geometric distributions as special cases among others. The construction and characteristics of the proposed bivariate distribution are presented along with estimation procedures for the model parameters based on maximum likelihood. The marginal and conditional laws are also studied. We present an application to the real data set where our model provides a better fit than other models., Comment: arXiv admin note: substantial text overlap with arXiv:1508.00219

In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized exponential distribution, the bivariate generalized exponential-poisson, -logarithmic, -binomial and -negative binomial distributions. We derive different properties of the new class of distributions. The EM algorithm is used to determine the maximum likelihood estimates of the parameters. We illustrate the usefulness of the new distributions by means of an application to a real data set., Comment: arXiv admin note: text overlap with arXiv:1507.07535

In this paper, we introduce a new class of bivariate distributions called the bivariate exponentiated extended Weibull distributions. The model introduced here is of Marshall-Olkin type. This new class of bivariate distributions contains several bivariate lifetime models. Some mathematical properties of the new class of distributions are studied. We provide the joint and conditional density functions, the joint cumulative distribution function and the joint survival function. Special bivariate distributions are investigated in some detail. The maximum likelihood estimators are obtained using the EM algorithm. We illustrate the usefulness of the new class by means of application to two real data sets., Comment: arXiv admin note: text overlap with arXiv:1501.03528 by other authors

This paper introduces a five-parameter lifetime model with increasing, decreasing, upside -down bathtub and bathtub shaped failure rate called as the McDonald Gompertz (McG) distribution. This new distribution extend the Gompertz, generalized Gompertz, generalized exponential, beta Gompertz and Kumaraswamy Gompertz distributions, among several other models. We obtain several properties of the McG distribution including moments, entropies, quantile and generating functions. We provide the density function of the order statistics and their moments. The parameter estimation is based on the usual maximum likelihood approach. We also provide the observed information matrix and discuss inferences issues. In the end, the flexibility and usefulness of the new distribution is illustrated by means of application to two real data sets.

In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power series, generalized exponential-power series, generalized linear failure rate-power series, exponentiated Weibull-power series, generalized modified Weibull-power series, generalized Gompertz-power series and exponentiated extended Weibull distributions as special cases. We obtain several properties of this new class of distributions such as Shannon entropy, mean residual life, hazard rate function, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented., Comment: Accepted for publication Ciencia e Natura Journal

The Weibull distribution is a very applicable model for the lifetime data. In this paper, we have investigated inference on the parameters of Weibull distribution based on record values. We first propose a simple and exact test and a confidence interval for the shape parameter. Then, in addition to a generalized confidence interval, a generalized test variable is derived for the scale parameter when the shape parameter is unknown. The paper presents a simple and exact joint confidence region as well. %for the scale and shape parameters. In all cases, simulation studies show that the proposed approaches are more satisfactory and reliable than previous methods. All proposed approaches are illustrated using a real example., Comment: Accepted for publication in SORT

The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order statistics of two runs statistics, and obtain their probability mass functions. In addition, the means and variances of the order statistics are derived using traditional conditional expectation., Comment: Accepted for publication in Model Assisted Statistics and Applications

In this paper, we consider the problem of constructing confidence interval for the correlation coefficient in a bivariate normal distribution. For this problem, we found fifteen approaches in literatures. Also, we have proposed a generalized confidence interval and a parametric bootstrap confidence interval. The coverage probabilities and expected lengths of these seventeen approaches are evaluated and compared via simulation study. In addition, robustness of the methods is considered in the comparisons by the non-normal distributions. Two real examples are given to illustrate the approaches., Comment: Accepted for publication Journal of Statistics Applications & Probability Letters

The Weibull distribution is a very applicable model for the lifetime data. For inference about two Weibull distributions using records, the shape parameters of the distributions are usually considered equal. However, there is not an appropriate method for comparing the shape parameters in the literature. Therefore, comparing the shape parameters of two Weibull distributions is very important. In this paper, we propose a method for constructing confidence interval and testing hypotheses about the ratio and difference of shape parameters using the concept of the generalized {\it p}-value and the generalized confidence interval. Simulation studies showed that our method is satisfactory. In the end, a real example is proposed to illustrate this method., Comment: Accepted for publication in Journal of Statistical Research of Iran

In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as beta-exponential and generalized Gompertz distributions as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing, and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the $k$th order moment, moment generating function, Shannon entropy, and the quantile measure are provided. We discuss maximum likelihood estimation of the BG parameters from one observed sample and derive the observed Fisher's information matrix. A simulation study is performed in order to investigate this proposed estimator for parameters. At the end, in order to show the BG distribution flexibility, an application using a real data set is presented., Comment: http://www.emis.de/journals/RCE/ingles/v37_1.html

Over the past decades, various methods for comparing the means of two log-normal have been proposed. Some of them are differing in terms of how the statistic test adjust to accept or to reject the null hypothesis. In this study, a new method of test for comparing the means of two log-normal populations is given through the generalized measure of evidence to have against the null hypothesis. However calculations of this method are simple, we find analytically that the considered method is doing well through comparing the size and power statistic test. In addition to the simulations, an example with real data is illustrated., Comment: http://www.scienpress.com/journal_focus.asp?main_id=68&Sub_id=IV&Issue=300

This paper deals with the estimation of reliability $R=P(Y

In situations where the sampling units in a study can be more easily ranked based on the measurement of an auxiliary variable, ranked set sampling provide unbiased estimators for the mean of a population that they are more efficient than unbiased estimator based on simple random sample. In this paper, we consider the Morgenstern type bivariate generalized exponential distribution (MTBGED) and obtain several unbiased estimators for a parameter mean of the marginal distribution of MTBGED based on different ranked set sampling schemes. The efficiency of all considered estimators are evaluate and has also been demonstrated with numerical illustrations., Comment: Accepted for publication SORT - Statistics and Operations Research Transactions; 2014

This note points out how confidence interval estimates for standard deviation transform into confidence interval estimates for the power of F-tests at fixed alternative means. An application is shown for the test of a two-sided hypothesis for the mean of a normal distribution.

A hypothesis testing and an interval estimation are studied for the common mean of several lognormal populations. Two methods are given based on the concept of generalized p-value and generalized confidence interval. These new methods are exact and can be used without restriction on sample sizes, number of populations, or difference hypotheses. A simulation study for coverage probability, size and power shown that the new methods are better than the existing methods. A numerical example is given with some real medical data.

In this article, we consider the problem of constructing the confidence interval and testing hypothesis for the common coefficient of variation (CV) of several normal populations. A new method is suggested using the concepts of generalized p-value and generalized confidence interval. Using this new method and a method proposed by Tian (2005), we obtain a shorter confidence interval for the common CV. This combination method has good properties in terms of length and coverage probability compared to other methods. A simulation study is performed to illustrate properties.. Finally, these methods are applied to two real data sets in medicine.

We introduce in this paper a new class of distributions which generalizes the linear failure rate (LFR) distribution and is obtained by compounding the LFR distribution and power series (PS) class of distributions. This new class of distributions is called the linear failure rate-power series (LFRPS) distributions and contains some new distributions such as linear failure rate geometric (LFRG) distribution, linear failure rate Poisson (LFRP) distribution, linear failure rate logarithmic (LFRL) distribution, linear failure rate binomial (LFRB) distribution and Raylight-power series (RPS) class of distributions. Some former works such as exponential-power series (EPS) class of distributions, exponential geometric (EG) distribution, exponential Poisson (EP) distribution and exponential logarithmic (EL) distribution are special cases of the new proposed model. The ability of the LFRPS class of distributions is in covering five possible hazard rate function i.e., increasing, decreasing, upside-down bathtub (unimodal), bathtub and increasing-decreasing-increasing shaped. Several properties of the LFRPS distributions such as moments, maximum likelihood estimation procedure via an EM-algorithm and inference for a large sample, are discussed in this paper. In order to show the flexibility and potentiality of the new class of distributions, the fitted results of the new class of distributions and some its submodels are compared using a real data set.

We introduce in this paper a new four-parameter generalized version of the linear failure rate (LFR) distribution which is called Beta-linear failure rate (BLFR) distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing, upside-down bathtub (unimodal) and bathtub-shaped failure rate function depending on its parameters. It includes some well-known lifetime distributions as special submodels. We provide a comprehensive account of the mathematical properties of the new distributions. In particular, A closed-form expressions for the density, cumulative distribution and hazard rate function of the BLFR is given. Also, the $r$th order moment of this distribution is derived. We discuss maximum likelihood estimation of the unknown parameters of the new model for complete sample and obtain an expression for Fishers information matrix. In the end, to show the flexibility of this distribution and illustrative purposes, an application using a real data set is presented.