Location-scale Regression Model Research Articles

On the Topp-Leone Generalized Power Weibull Distribution: Properties, Applications and Regression

Abstract The Topp-Leone generalized power Weibull distribution, which is an extension of generalized power Weibull, is proposed and its properties explored. The failure rate of the proposed distribution exhibits increasing, reversed J, upside-down bathtub, and bathtub shapes. Some statistical properties are obtained: quantile function, moments, moment generating function, incomplete moment, mean and median deviations, mean residual life function, and Lorenz as well as Bonferroni curves. The maximum likelihood estimation approach is deployed to estimate the model parameters. Simulation studies are conducted to evaluate the performance and accuracy of the maximum likelihood estimates of the model parameters. Applications of the model to real datasets are presented. A location-scale regression model is also developed for the proposed model and its application has been demonstrated with a real dataset. Keywords: Bonferroni, Deviation, Mimicked, Simulation, and Upside-down Bathtub.

Modified Ramos-Louzada-G family with baseline Weibull distribution: Properties, characterizations, regression, and applications

The paper introduced a novel family of distributions, called the Kumaraswamy Ramos-Louzada-G (KumRL-G) class, focusing on the five-parameter Kumaraswamy Ramos-Louzada Weibull (KumRLW) distribution. This new family of distributions, which includes existing and numerous new sub-models, offers improved flexibility and accuracy in modeling and analyzing survival data. Key statistical properties, including quantile function, moments, and entropy measures underlying the distribution have been derived, and characterizations have also been provided based on the ratio of two truncated moments and the hazard rate function. The maximum likelihood estimation (MLE) is employed to estimate the parameters of the proposed probability distribution, and Monte Carlo simulation analysis is performed to demonstrate the effectiveness of this method. The significance and adaptability of the new family of distributions are revealed through applications to COVID-19 and survival rate to age 65 of male cohort datasets from Ghana, Nigeria, and Canada. A new location-scale regression model was subsequently formulated from the new KumRLW distribution. Its practicality was demonstrated using survival data on hypertension from Ghana with gender as a covariate. The regression analysis showed that gender is a significant factor in the length of time before hypertension develops. The new KumRL-G family with baseline Weibull distributions provides more flexibility and improved fit in modeling various shapes and behaviors in the survival datasets surpassing its existing sub-models and other notable distributions.

A federated data fusion-based prognostic model for applications with multi-stream incomplete signals

Most prognostic methods require a decent amount of data for model training. In reality, however, the amount of historical data owned by a single organization might be small or not large enough to train a reliable prognostic model. To address this challenge, this article proposes a federated prognostic model that allows multiple users to jointly construct a failure time prediction model using their multi-stream, high-dimensional, and incomplete data while keeping each user’s data local and confidential. The prognostic model first employs multivariate functional principal component analysis to fuse the multi-stream degradation signals. Then, the fused features coupled with the times-to-failure are utilized to build a (log)-location-scale regression model for failure prediction. To estimate parameters using distributed datasets and keep the data privacy of all participants, we propose a new federated algorithm for feature extraction. Numerical studies indicate that the performance of the proposed model is the same as that of classic non-federated prognostic models and is better than that of the models constructed by each user itself.

New Weighted Burr XII Distribution: Statistical Properties, Applications, and Regression

In this study, a three-parameter modification of the Burr XII distribution has been developed through the integration of the weighted version of the alpha power transformation family of distributions. This newly introduced model, termed the modified alpha power-transformed Burr XII distribution, exhibits the unique ability to effectively model decreasing, right-skewed, or unimodal densities. The paper systematically elucidates various statistical properties of the proposed distribution. The estimation of parameters was obtained using maximum likelihood estimation. The estimator has been evaluated for consistency through simulation studies. To gauge the practical applicability of the proposed distribution, two distinct datasets have been employed. Comparative analyses involving six alternative distributions unequivocally demonstrate that the modified alpha power-transformed Burr XII distribution provides a better fit. Additionally, a noteworthy extension is introduced in the form of a location-scale regression model known as the log-modified alpha power-transformed Burr XII model. This model is subsequently applied to a dataset related to stock market liquidity. The findings underscore the enhanced fitting capabilities of the proposed model in comparison to existing distributions, providing valuable insights for applications in financial modelling and analysis.

Secant Kumaraswamy Family of Distributions: Properties, Regression Model, and Applications

In this study, Secant Kumaraswamy family of distributions is proposed and studied. This is motivated by the fact that no one distribution can model all types of data from different fields. Therefore, there is the need to develop distributions with desirable properties and flexible enough for modelling data exhibiting different characteristics. Some properties of the new family of distributions, including the quantile function, moments, moment generating function, and mean residual life function, are derived. Five special cases of the family of distributions are presented, and their flexibility is shown by the varying degrees of skewness and kurtosis and nonmonotonic hazard rates. The maximum likelihood estimation method is used to obtain estimators of the family of distributions. Two location-scale regression models are developed for the Secant Kumaraswamy Weibull distribution, which is a special case of the family of distributions. Six different real datasets are used to demonstrate the usefulness of the family of distributions and the regression models. The results show that the family of distributions can be used to model real datasets.

The Logistic Burr XII Distribution: Properties and Applications to Income Data

We define and study the four-parameter logistic Burr XII distribution. It is obtained by inserting the three-parameter Burr XII distribution as the baseline in the logistic-X family and may be a useful alternative method to model income distribution and could be applied to other areas. We illustrate that the new distribution can have decreasing and upside-down-bathtub hazard functions and that its density function is an infinite linear combination of Burr XII densities. Some mathematical properties of the proposed model are determined, such as the quantile function, ordinary and incomplete moments, and generating function. We also obtain the maximum likelihood estimators of the model parameters and perform a Monte Carlo simulation study. Further, we present a parametric regression model based on the introduced distribution as an alternative to the location-scale regression model. The potentiality of the new distribution is illustrated by means of two applications to income data sets.

Fast estimation of mixed-effects location-scale regression models.

As a result of advances in data collection technology and study design, modern longitudinal datasets can be much larger than they historically have been. Such "intensive" longitudinal datasets are rich enough to allow for detailed modeling of the variance of a response as well as the mean, and a flexible class of models called mixed-effects location-scale (MELS) regression models are commonly used to do so. However, fitting MELS models can pose computational challenges related to the numerical evaluation of multi-dimensional integrals; the slow runtime of current methods is inconvenient for data analysis and makes bootstrap inference impractical. In this paper, we introduce a new fitting technique, called FastRegLS, that is considerably faster than existing techniques while still providing consistent estimators for the model parameters.

Harmonic Mixture Weibull-G Family of Distributions: Properties, Regression and Applications to Medical Data

In recent years, the developments of new families of probability distributions have received greater attention as a result of desirable properties they exhibit in the modelling of data sets. The Harmonic Mixture Weibull-G family of distributions was developed in this study. The statistical properties were comprehensively presented and five special distributions developed from the family. The hazard functions of the special distributions were shown to exhibit various forms of monotone and nonmonotone shapes. The applications of the developed family to real data sets in medical studies revealed that the special distribution (Harmonic mixture Weibul Weibull distribution) provided a better fit to the data sets than other competitive models. A location-scale regression model was developed from the family and its application demonstrated using survival time data of hypertensive patients.

Tangent Topp-Leone Family of Distributions

We introduce the tangent Topp-Leone family of distributions in this study and derive some of its statistical properties. Further, we develop five special distributions and a location-scale regression model based on the new proposed tangent Topp-Leone Weibull distribution. Three real datasets are used to demonstrate the usefulness and flexibility of the developed models in comparison with other existing competing models. The study reveals that the proposed tangent Topp-Leone-Weibull perform better than competing models for the given datasets. The proposed log tangent Topp-Leone-Weibull regression model also performs better than competing models for a given dataset.

The Beta Power Muth Distribution: Regression Modeling, Properties and Data Analysis

In this paper, we propose a new flexible lifetime distribution. The proposed distribution will be referred to as beta power Muth distribution. It can be used to model increasing, decreasing, bathtub shaped or upside-down bathtub hazard rates. Some properties of the new model are obtained including moments, quantile function and moments of the order statistics. The unknown model parameters are estimated by the maximum likelihood method of estimation. A Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates. Two reliability data sets are applied to illustrate the usefulness and flexibility of the proposed model. In addition, we introduce a new location-scale regression model based on the logarithm of the proposed distribution and provide a real data application.

Estimation of the volume under a ROC surface in presence of covariates

A new method to adjust for covariate effects in the estimation of volume under a ROC surface (VUS) is presented. The method is based on the induced-regression methodology, which uses location-scale regression models to explain the relation between the test results and the covariate(s). For the estimation of the models, it is proposed to use a semiparametric generalized estimating equations (GEE) approach if the parametric forms of the mean and variance functions are specified. Alternatively, a nonparametric method is proposed, based on local linear regression (LL). In order to estimate the covariate-specific VUS, a covariate-specific Mann-Whitney representation of VUS is used, and working samples constructed after fitting the location-scale models by the GEE or LL approach. This leads to new MW-GEE and MW-LL covariate-specific VUS estimators. The asymptotic behavior of the new estimators is investigated. More precisely, their mean squared consistency is proved. Moreover, the performance of the estimators in finite samples is explored through several simulation experiments, and an illustration, based on data from the Alzheimer's Disease Neuroimaging Initiative, is provided.

Robust consistent estimators for ROC curves with covariates

The Receiver Operating Characteristic (ROC) curve is a useful tool to measure the classification capability of a continuous variable to assess the accuracy of a medical test that distinguishes between two conditions. Sometimes, covariates related to the diagnostic variable may increase the discriminating power of the ROC curve. Due to the lack of stability of classical ROC curves estimators to outliers, we introduce a procedure to obtain robust estimators in presence of covariates. The considered proposal focusses on a semiparametric approach which robustly fits a location-scale regression model to the diagnostic variable and considers robust adaptive empirical estimators of the regression residuals. The uniform consistency of the proposal is derived under mild assumptions. A Monte Carlo study is carried out to compare the performance of the robust proposed estimators with the classical ones both, in clean and contaminated samples. A real data set is also analysed.

A Log-Beta Rayleigh Lomax Regression Model

For the first time, a location-scale regression model based on the logarithm of an extended Raleigh Lomax distribution which has the ability to deal and model of any survival data than classical regression model is introduced. We obtain the estimate for the model parameters using the method of maximum likelihood by considering breast cancer data. In addition, normal probability plot of the residual is used to detect the outliers and evaluate model assumptions. We use a real data set to illustrate the performance of the new model, some of its submodels and classical models consider in the study. Also, we perform the statistics AIC, BIC and CAIC to select the most appropriate model among those regression models considered in the study.

Robust and flexible inference for the covariate-specific receiver operating characteristic curve.

Diagnostic tests are of critical importance in health care and medical research. Motivated by the impact that atypical and outlying test outcomes might have on the assessment of the discriminatory ability of a diagnostic test, we develop a robust and flexible model for conducting inference about the covariate-specific receiver operating characteristic (ROC) curve that safeguards against outlying test results while also accommodating for possible nonlinear effects of the covariates. Specifically, we postulate a location-scale regression model for the test outcomes in both the diseased and nondiseased populations, combining additive regression B-splines and M-estimation for the regression function, while the distribution of the error term is estimated via a weighted empirical distribution function of the standardized residuals. The results of the simulation study show that our approach successfully recovers the true covariate-specific area under the ROC curve on a variety of conceivable test outcomes contamination scenarios. Our method is applied to a dataset derived from a prostate cancer study where we seek to assess the ability of the Prostate Health Index to discriminate between men with and without Gleason 7 or above prostate cancer, and if and how such discriminatory capacity changes with age.

A New Flexible Family of Continuous Distributions: The Additive Odd-G Family

This paper introduces a new family of distributions based on the additive model structure. Three submodels of the proposed family are studied in detail. Two simulation studies were performed to discuss the maximum likelihood estimators of the model parameters. The log location-scale regression model based on a new generalization of the Weibull distribution is introduced. Three datasets were used to show the importance of the proposed family. Based on the empirical results, we concluded that the proposed family is quite competitive compared to other models.

A New Extension of Fréchet Distribution with Regression Models, Residual Analysis and Characterizations

A new log location-scale regression model with applications to voltage and Stanford heart transplant data sets is presented and studied. The martingale and modified deviance residuals to detect outliers and evaluate the model assumptions are defined. The new model can be very useful in analysing and modeling real data and provides more better fits than other regression models such as the log odd log-logistic generalized half-normal, the log beta generalized half-normal, the log generalized half-normal, the log-Topp-Leone odd log- logistic-Weibull and the log-Weibull models. Characterizations based on truncated moments as well as in terms of the reverse hazard function are presented. The maximum likelihood method is discussed to estimate the model parameters by means of a graphical Monte Carlo simulation study. The flexibility of the new model illustrated by means of four real data sets.

A Study on A New Type 1 Half-Logistic Family of Distributions and Its Applications

In this paper, we propose a new class of continuous distributions with two extra shape parameters called the a new type I half logistic-G family of distributions. Some of important properties including ordinary moments, quantiles, moment generating function, mean deviation, moment of residual life, moment of reversed residual life, order statistics and extreme value are obtained. To estimate the model parameters, the maximum likelihood method is also applied by means of Monte Carlo simulation study. A new location-scale regression model based on the new type I half logistic-Weibull distribution is then introduced. Applications of the proposed family is demonstrated in many fields such as survival analysis and univariate data fitting. Empirical results show that the proposed models provide better fits than other well-known classes of distributions in many application fields.

The Odds Exponential-Pareto IV Distribution: Regression Model and Application.

This article introduces the odds exponential-Pareto IV distribution, which belongs to the odds family of distributions. We studied the statistical properties of this new distribution. The odds exponential-Pareto IV distribution provided decreasing, increasing, and upside-down hazard functions. We employed the maximum likelihood method to estimate the distribution parameters. The estimators performance was assessed by conducting simulation studies. A new log location-scale regression model based on the odds exponential-Pareto IV distribution was also introduced. Parameter estimates of the proposed model were obtained using both maximum likelihood and jackknife methods for right-censored data. Real data sets were analyzed under the odds exponential-Pareto IV distribution and log odds exponential-Pareto IV regression model to show their flexibility and potentiality.

The Generalized Kumaraswamy-G Family of Distributions

We propose a new class of continuous distributions called the generalized Kumaraswamy-G family which extends the Kumaraswamy-G family defined by Cordeiro and de Castro [1]. Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi entropy, order statistics and characterizations are derived. The new location-scale regression model is introduced based on the new generated distribution. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.

Technological change, technological catch-up and export orientation: evidence from Latin American Countries

The paper examines in a nonparametric frontier framework the effect of exports on Latin American countries’ technological change and technological catch-up levels over the period 1950–2014. Based on the probabilistic approach of nonparametric production efficiency measurement, we apply time-dependent conditional full and partial efficiency estimators to evaluate countries’ export orientation policies over the examined period. The results reveal that the effect of countries’ export activity on their technological change and technological catch-up levels is nonlinear. Overall our findings suggest that up to a certain point, lower export shares enhance countries’ technological catch-up levels. The results also reveal that higher export shares affect positively their technological change levels. Finally, in a second stage analysis we apply a location-scale regression model in order to estimate the idiosyncratic part of the estimated production efficiencies. This measure is a proxy of Solow’s residual accounting for aggregate effects of other factors not included in our estimation.