scholarly journals A New Truncated Muth Generated Family of Distributions with Applications

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Abdullah M. Almarashi ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Statistical Models ◽  
Simulation Analysis ◽  
Weibull Model ◽  
Maximum Likelihood Procedure ◽  
Peak Asymmetry ◽  
Moment Measures ◽  
Competing Models ◽  
Real World Datasets ◽  
Applied Fields ◽  
Generated Family

In recent years, the Muth distribution has been used for the construction of accurate statistical models, with applications in various applied fields. In this paper, we use a truncated-composed scheme to create a new unit Muth distribution, from which we motivate a more general family of continuous distributions called the truncated Muth generated family. The key benefits of this family are its analytical simplicity, connections with the exponential generated family, and flexibility conferred on any parental distribution. In particular, it improves the capability of the functions of the parental distribution, enhancing their peak, asymmetry, tail, and flatness levels, among others. The characteristics of quantile and moment measures and functions of the truncated Muth generated family are described in detail. As a concrete example, a particular distribution that extends the Weibull distribution is highlighted. In an applied part, the parameters are calculated using the maximum likelihood procedure. We use a comprehensive simulation analysis to demonstrate the accuracy of the derived estimates. The revised Weibull model is then used to fit two real-world datasets. The new model is shown to be more suited to these datasets than other competing models.

scholarly journals Application to Engineering and Medical Data Using Three-Parameter Exponential Model

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Waleed Almutiry ◽  
Amani Abdullah Alahmadi ◽  
Ibrahim Elbatal ◽  
Ibrahim E. Ragab ◽  
Oluwafemi Samson Balogun ◽  
...  
Keyword(s):  
Simulation Analysis ◽  
Residual Life ◽  
Quantile Function ◽  
Exponential Model ◽  
Statistical Characteristics ◽  
Mean Residual Life ◽  
New Model ◽  
Conditional Moments ◽  
Mean Inactivity Time ◽  
Real World Datasets

This paper is devoted to a new lifetime distribution having three parameters by compound the exponential model and the transmuted Topp-Leone-G. The new proposed model is called the transmuted Topp-Leone exponential model; it is useful in lifetime data and reliability. The new model is very flexible; its pdf can be right skewness, unimodal, and decreasing shaped, but the hrf of the suggested model can be unimodal, constant, and decreasing. Numerous statistical characteristics of the new model, notably the quantile function, moments, incomplete moments, conditional moments, mean residual life, mean inactivity time, and entropy are produced and investigated. The system’s parameters are estimated using the maximum likelihood approach. All estimators should be theoretically convergent, which is supported by a simulation analysis. Finally, two real-world datasets from the engineering and medical disciplines explore the new model’s relevance and adaptability in comparison to the alternatives models such as the beta exponential, the Marshall–Olkin generalized exponential, the exponentiated Weibull, the modified Weibull, and the transmuted Burr type X models.

scholarly journals From theories to models to predictions: A Bayesian model comparison approach

2017 ◽  
Author(s):  
Jeffrey Rouder ◽  
Julia M. Haaf ◽  
Frederik Aust
Keyword(s):  
Statistical Models ◽  
Bayesian Model ◽  
Model Comparison ◽  
Bayes Factor ◽  
Significance Testing ◽  
Bayesian Model Comparison ◽  
Comparison Approach ◽  
Competing Models ◽  
Competing Hypotheses

A key goal in research is to use data to assess competing hypotheses or theories. Analternative to the conventional significance testing is Bayesian model comparison. The mainidea is that competing theories are represented by statistical models. In the Bayesianframework, these models then yield predictions about data even before the data are seen.How well the data match the predictions under competing models may be calculated, andthe ratio of these matches—the Bayes factor—is used to assess the evidence for one modelcompared to another. We illustrate the process of going from theories to models and topredictions in the context of two hypothetical examples about how exposure to media affectsattitudes toward refugees.

scholarly journals Odd Generalized N-H Generated Family of Distributions with Application to Exponential Model

2020 ◽  
pp. 53-71
Author(s):  
Zubair Ahmad ◽  
M. Elgarhy ◽  
G.G. Hamedani ◽  
Nadeem Shafique Butt
Keyword(s):  
Real Data ◽  
Quantile Function ◽  
Exponential Model ◽  
Mean Deviation ◽  
Parameter Estimates ◽  
Data Sets ◽  
New Family ◽  
Maximum Likelihood Procedure ◽  
Generated Family ◽  
Family Of Distributions

A new family of distributions called the odd generalized N-H is introduced and studied. Four new special models are presented. Some mathematical properties of the odd generalized N-H family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Characterizations based on the truncated moments, hazard function and conditional expectations are presented for the generated family. Parameter estimates of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family.

scholarly journals A New Exponential-X Family: Modeling Extreme Value Data in the Finance Sector

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
Rasool Roozegar ◽  
Morad Alizadeh ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Statistical Models ◽  
Claims Data ◽  
Maximum Likelihood Estimators ◽  
Weibull Model ◽  
Insurance Claims Data ◽  
Practical Analysis ◽  
Heavy Tailed ◽  
Modeling Data

In this paper, a family of statistical models, namely, a new exponential-X family is proposed. A subcase of the introduced family, called the new exponential-Weibull (NE-Weibull) model, is studied. The NE-Weibull model is very competent and possesses heavy-tailed properties. The maximum likelihood estimators of its parameters are derived. The consistency and efficiency of these estimators are assessed in a brief simulation study. Finally, the effectiveness of the NE-Weibull distribution is illustrated by modeling real insurance claims data. The practical analysis shows that the NE-Weibull distribution outclassed other distributions and it can be a better choice for modeling data in the finance sector.

scholarly journals The Arctan-X Family of Distributions: Properties, Simulation, and Applications to Actuarial Sciences

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Ibrahim Alkhairy ◽  
M. Nagy ◽  
Abdisalam Hassan Muse ◽  
Eslam Hussam
Keyword(s):  
Weibull Distribution ◽  
Model Comparison ◽  
Simulation Analysis ◽  
Likelihood Estimation ◽  
Weibull Model ◽  
Trigonometric Function ◽  
Data Sets ◽  
Data Set ◽  
Heavy Tailed ◽  
Family Of Distributions

The purpose of this paper is to investigate a new family of distributions based on an inverse trigonometric function known as the arctangent function. In the context of actuarial science, heavy-tailed probability distributions are immensely beneficial and play an important role in modelling data sets. Actuaries are committed to finding for such distributions in order to get an excellent fit to complex economic and actuarial data sets. The current research takes a look at a popular method for generating new distributions which are excellent candidates for dealing with heavy-tailed data. The proposed family of distributions is known as the Arctan-X family of distributions and is introduced using an inverse trigonometric function. For the specific purpose of the show of strength, we studied the Arctan-Weibull distribution as a special case of the developed family. To estimate the parameters of the Arctan-Weibull distribution, the frequentist approach, i.e., maximum likelihood estimation, is used. A rigorous Monte Carlo simulation analysis is used to determine the efficiency of the obtained estimators. The Arctan-Weibull model is demonstrated using a real-world insurance data set. The Arctan-Weibull is compared to well-known two-, three-, and four-parameter competitors. Among the competing distributions are Weibull, Kappa, Burr-XII, and beta-Weibull. For model comparison, we used the most precise tests used to know whether the Arctan-Weibull distribution is more useful than competing models.

On the Behavior of Statistical Models Used for Design

1976 ◽  
Vol 98 (2) ◽  
pp. 601-606 ◽  
Author(s):  
P. H. Wirsching
Keyword(s):  
Statistical Models ◽  
Random Variable ◽  
Upper Bounds ◽  
Probability Models ◽  
Tail Probabilities ◽  
Structural Element ◽  
Probability Estimates ◽  
Power Models ◽  
Competing Models ◽  
Two Parameter

In probabilistic design, it is common practice to use two parameter statistical models (e.g., normal, lognormal) to describe random design factors. However, given a random sample of data, it is often difficult to distinguish which of several competing models provides the best description. It is demonstrated herein that the choice of model has a profound effect on probability estimates, particularly in the tails of the distributions. Given only the mean and standard deviation of a random variable, the Tchebycheff or Camp-Meidell inequalities can be used to provide upper-bound estimates of probabilities. However, these inequalities are usually too weak for design purposes. Probability models which yield more reasonable results are proposed. The two parameter exponential and power models are proposed for quasi-upper bounds of right and left tail probabilities, respectively. The exponential and power models are used for stress and strength, respectively, to derive, from inference theory, quasi-upper bounds for probability of failure of a structural element.

scholarly journals Survival Following Road Traffic Accidents in a Level-I Trauma Center, Parametric versus Semi-Parametric Survival Models

2021 ◽  
Keyword(s):  
Multivariate Analysis ◽  
Survival Analysis ◽  
Statistical Models ◽  
Trauma Center ◽  
Proportional Hazards ◽  
Road Traffic ◽  
Weibull Model ◽  
Parametric Models ◽  
Level I ◽  
Parametric Survival

Background: Simulation studies present an important statistical tool to investigate the performance, properties, and adequacy of statistical models in pre-specified situations. The proportional hazards model of survival analysis is one of the most important statistical models in medical studies. This study aimed to investigate the underlying one-month survival of road traffic accident (RTA) victims in a Level 1 Trauma Center in Iran using parametric and semi-parametric survival analysis models from the viewpoint of post-crash care-provider in 2017. Materials and Methods: This retrospective cohort study (restudy) was conducted at Level-I Trauma Center of Shiraz, Iran, from January to December 2017. Considering the fact that certain covariates acting on survival may take a non-homogenous risk pattern leading to the violation of proportional hazards assumption in Cox-PH, the parametric survival modeling was employed to inspect the multiplicative effect of all covariates on the hazard. Distributions of choice were Exponential, Weibull and Lognormal. Parameters were estimated using the Akaike Results: Survival analysis was conducted on 8,621 individuals for whom the length of stay (observation period) was between 1 and 89 days. In total, 141 death occurred during this time. The log-rank test revealed inequality of survival functions across various categories of age, injury mechanism, injured body region, injury severity score, and nosocomial infections. Although the risk level in the Cox model is almost the same as that in the results of the parametric models, the Weibull model in the multivariate analysis yields better results, according to the Akaike criterion. Conclusion: In multivariate analysis, parametric models were more efficient than other models. Some results were similar in both parametric and semi-parametric models. In general, parametric models and among them the Weibull model was more efficient than other models.

Facet Topography and Dislocation Structure as a Possible Source for Electrical Heterogeneity in [001] TILT Bicrystals of YBa2Cu3O7-δ

1996 ◽  
Vol 54 ◽  
pp. 338-339
Author(s):  
I-Fei Tsu ◽  
D.L. Kaiser ◽  
S.E. Babcock
Keyword(s):  
Grain Boundary ◽  
Critical Current Density ◽  
Critical Current ◽  
Current Density ◽  
Electromagnetic Properties ◽  
Length Scale ◽  
Density Values ◽  
Current Densities ◽  
Applied Fields ◽  
A Current

A current theme in the study of the critical current density behavior of YBa2Cu3O7-δ (YBCO) grain boundaries is that their electromagnetic properties are heterogeneous on various length scales ranging from 10s of microns to ˜ 1 Å. Recently, combined electromagnetic and TEM studies on four flux-grown bicrystals have demonstrated a direct correlation between the length scale of the boundaries’ saw-tooth facet configurations and the apparent length scale of the electrical heterogeneity. In that work, enhanced critical current densities are observed at applied fields where the facet period is commensurate with the spacing of the Abrikosov flux vortices which must be pinned if higher critical current density values are recorded. To understand the microstructural origin of the flux pinning, the grain boundary topography and grain boundary dislocation (GBD) network structure of [001] tilt YBCO bicrystals were studied by TEM and HRTEM.

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