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.

scholarly journals Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

scholarly journals A New Flexible Bathtub-Shaped Modification of the Weibull Model: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Qinghu Liao ◽  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Weibull Model ◽  
Rate Function ◽  
Model Parameters ◽  
Hazard Functions ◽  
Practical Applications ◽  
Nonnested Models

Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distribution may be called a new flexible extended Weibull distribution. Corresponding hazard rate function of the proposed distribution shows flexible (monotone and nonmonotone) shapes. Three different characterizations along with some mathematical properties are provided. We also consider the maximum likelihood estimation procedure to estimate the model parameters. For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.

An Accurate Substitution Method To Minimize Left Censoring Bias in Serum Steroid Measurements

Endocrinology ◽  
2019 ◽  
Vol 160 (10) ◽  
pp. 2395-2400 ◽  
Author(s):  
David J Handelsman ◽  
Lam P Ly
Keyword(s):  
Data Analysis ◽  
Ad Hoc ◽  
Likelihood Estimation ◽  
Large Data ◽  
Serum Testosterone ◽  
Accurate Method ◽  
Estimation Methods ◽  
Data Sets ◽  
Full Data ◽  
Data Set

Abstract Hormone assay results below the assay detection limit (DL) can introduce bias into quantitative analysis. Although complex maximum likelihood estimation methods exist, they are not widely used, whereas simple substitution methods are often used ad hoc to replace the undetectable (UD) results with numeric values to facilitate data analysis with the full data set. However, the bias of substitution methods for steroid measurements is not reported. Using a large data set (n = 2896) of serum testosterone (T), DHT, estradiol (E2) concentrations from healthy men, we created modified data sets with increasing proportions of UD samples (≤40%) to which we applied five different substitution methods (deleting UD samples as missing and substituting UD sample with DL, DL/√2, DL/2, or 0) to calculate univariate descriptive statistics (mean, SD) or bivariate correlations. For all three steroids and for univariate as well as bivariate statistics, bias increased progressively with increasing proportion of UD samples. Bias was worst when UD samples were deleted or substituted with 0 and least when UD samples were substituted with DL/√2, whereas the other methods (DL or DL/2) displayed intermediate bias. Similar findings were replicated in randomly drawn small subsets of 25, 50, and 100. Hence, we propose that in steroid hormone data with ≤40% UD samples, substituting UD with DL/√2 is a simple, versatile, and reasonably accurate method to minimize left censoring bias, allowing for data analysis with the full data set.

A practical introduction to methods for analyzing longitudinal data in the presence of missing data using a marijuana price survey

2015 ◽  
Vol 5 (2) ◽  
pp. 137-148 ◽  
Author(s):  
Jeremy N.V Miles ◽  
Priscillia Hunt
Keyword(s):  
Missing Data ◽  
Statistical Power ◽  
Criminal Psychology ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Applied Psychology ◽  
Artificial Data ◽  
Data Set ◽  
Content Type ◽  
Biased Estimates

Purpose – In applied psychology research settings, such as criminal psychology, missing data are to be expected. Missing data can cause problems with both biased estimates and lack of statistical power. The paper aims to discuss these issues. Design/methodology/approach – Recently, sophisticated methods for appropriately dealing with missing data, so as to minimize bias and to maximize power have been developed. In this paper the authors use an artificial data set to demonstrate the problems that can arise with missing data, and make naïve attempts to handle data sets where some data are missing. Findings – With the artificial data set, and a data set comprising of the results of a survey investigating prices paid for recreational and medical marijuana, the authors demonstrate the use of multiple imputation and maximum likelihood estimation for obtaining appropriate estimates and standard errors when data are missing. Originality/value – Missing data are ubiquitous in applied research. This paper demonstrates that techniques for handling missing data are accessible and should be employed by researchers.

scholarly journals CIM-seq

2021 ◽  
Author(s):  
Nathanael Andrews ◽  
Martin Enge
Keyword(s):  
Single Cell ◽  
Single Cells ◽  
Likelihood Estimation ◽  
Cell Types ◽  
Data Sets ◽  
Target Tissue ◽  
Data Set ◽  
Rnaseq Data ◽  
The Given ◽  
Cell Data

Abstract CIM-seq is a tool for deconvoluting RNA-seq data from cell multiplets (clusters of two or more cells) in order to identify physically interacting cell in a given tissue. The method requires two RNAseq data sets from the same tissue: one of single cells to be used as a reference, and one of cell multiplets to be deconvoluted. CIM-seq is compatible with both droplet based sequencing methods, such as Chromium Single Cell 3′ Kits from 10x genomics; and plate based methods, such as Smartseq2. The pipeline consists of three parts: 1) Dissociation of the target tissue, FACS sorting of single cells and multiplets, and conventional scRNA-seq 2) Feature selection and clustering of cell types in the single cell data set - generating a blueprint of transcriptional profiles in the given tissue 3) Computational deconvolution of multiplets through a maximum likelihood estimation (MLE) to determine the most likely cell type constituents of each multiplet.

scholarly journals Closed form expressions for moments of the beta Weibull distribution

2011 ◽  
Vol 83 (2) ◽  
pp. 357-373 ◽  
Author(s):  
Gauss M Cordeiro ◽  
Alexandre B Simas ◽  
Borko D Stošic
Keyword(s):  
Weibull Distribution ◽  
Closed Form ◽  
Cumulative Distribution Function ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Set ◽  
Expected Information ◽  
Beta Weibull Distribution

The beta Weibull distribution was first introduced by Famoye et al. (2005) and studied by these authors and Lee et al. (2007). However, they do not give explicit expressions for the moments. In this article, we derive explicit closed form expressions for the moments of this distribution, which generalize results available in the literature for some sub-models. We also obtain expansions for the cumulative distribution function and Rényi entropy. Further, we discuss maximum likelihood estimation and provide formulae for the elements of the expected information matrix. We also demonstrate the usefulness of this distribution on a real data set.

scholarly journals The Adjusted Log-logistic Generalized Exponential Distribution with Application to Lifetime Data

2017 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
I. E. Okorie ◽  
A. C. Akpanta ◽  
J. Ohakwe ◽  
D. C. Chikezie ◽  
C. U. Onyemachi ◽  
...  
Keyword(s):  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
Generalized Exponential Distribution ◽  
Data Set ◽  
Method Of Maximum Likelihood ◽  
The One ◽  
Special Case

This paper introduces a new generator of probability distribution-the adjusted log-logistic generalized (ALLoG) distribution and a new extension of the standard one parameter exponential distribution called the adjusted log-logistic generalized exponential (ALLoGExp) distribution. The ALLoGExp distribution is a special case of the ALLoG distribution and we have provided some of its statistical and reliability properties. Notably, the failure rate could be monotonically decreasing, increasing or upside-down bathtub shaped depending on the value of the parameters $\delta$ and $\theta$. The method of maximum likelihood estimation was proposed to estimate the model parameters. The importance and flexibility of he ALLoGExp distribution was demonstrated with a real and uncensored lifetime data set and its fit was compared with five other exponential related distributions. The results obtained from the model fittings shows that the ALLoGExp distribution provides a reasonably better fit than the one based on the other fitted distributions. The ALLoGExp distribution is therefore ecommended for effective modelling of lifetime data sets.

scholarly journals New defective models based on the Kumaraswamy family of distributions with application to cancer data sets

2015 ◽  
Vol 26 (4) ◽  
pp. 1737-1755 ◽  
Author(s):  
Ricardo Rocha ◽  
Saralees Nadarajah ◽  
Vera Tomazella ◽  
Francisco Louzada ◽  
Amanda Eudes
Keyword(s):  
Likelihood Estimation ◽  
Data Sets ◽  
Inverse Gaussian ◽  
Finite Sample ◽  
Gaussian Distributions ◽  
Cancer Data ◽  
Estimated Parameters ◽  
Cure Fraction ◽  
Modeling Data ◽  
Family Of Distributions

An alternative to the standard mixture model is proposed for modeling data containing cured elements or a cure fraction. This approach is based on the use of defective distributions to estimate the cure fraction as a function of the estimated parameters. In the literature there are just two of these distributions: the Gompertz and the inverse Gaussian. Here, we propose two new defective distributions: the Kumaraswamy Gompertz and Kumaraswamy inverse Gaussian distributions, extensions of the Gompertz and inverse Gaussian distributions under the Kumaraswamy family of distributions. We show in fact that if a distribution is defective, then its extension under the Kumaraswamy family is defective too. We consider maximum likelihood estimation of the extensions and check its finite sample performance. We use three real cancer data sets to show that the new defective distributions offer better fits than baseline distributions.

scholarly journals The Skewed-Elliptical Log-Linear Birnbaum–Saunders Alpha-Power Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1297
Author(s):  
Guillermo Martínez-Flórez ◽  
Heleno Bolfarine ◽  
Yolanda M. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Power Distribution ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Alpha Power ◽  
Data Set ◽  
Special Cases ◽  
Standard Error Estimation ◽  
Log Linear

In this paper, the skew-elliptical sinh-alpha-power distribution is developed as a natural follow-up to the skew-elliptical log-linear Birnbaum–Saunders alpha-power distribution, previously studied in the literature. Special cases include the ordinary log-linear Birnbaum–Saunders and skewed log-linear Birnbaum–Saunders distributions. As shown, it is able to surpass the ordinary sinh-normal models when fitting data sets with high (above the expected with the sinh-normal) degrees of asymmetry. Maximum likelihood estimation is developed with the inverse of the observed information matrix used for standard error estimation. Large sample properties of the maximum likelihood estimators such as consistency and asymptotic normality are established. An application is reported for the data set previously analyzed in the literature, where performance of the new distribution is shown when compared with other proposed alternative models.

scholarly journals A generalization to the log-inverse Weibull distribution and its applications in cancer research

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
C. Satheesh Kumar ◽  
Subha R. Nair
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Life ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Reliability Function ◽  
Rate Function ◽  
Data Sets ◽  
Inverse Weibull Distribution

AbstractIn this paper we consider a generalization of a log-transformed version of the inverse Weibull distribution. Several theoretical properties of the distribution are studied in detail including expressions for its probability density function, reliability function, hazard rate function, quantile function, characteristic function, raw moments, percentile measures, entropy measures, median, mode etc. Certain structural properties of the distribution along with expressions for reliability measures as well as the distribution and moments of order statistics are obtained. Also we discuss the maximum likelihood estimation of the parameters of the proposed distribution and illustrate the usefulness of the model through real life examples. In addition, the asymptotic behaviour of the maximum likelihood estimators are examined with the help of simulated data sets.

Sign in / Sign up

Export Citation Format

Share Document