Quadratic Rank Transmutation Map Research Articles

Statistical analysis for progressive stress accelerated life test with transmutation Weibull distribution

The Transmutation Weibull distribution is derived from the quadratic rank transmutation map of the Weibull distribution. This distribution integrates the high adaptability of the Weibull distribution in engineering and materials fields, and has great potential utility for modeling lifetime data. Therefore, the article explores the progressive stress accelerated life test model for components under the Transmutation Weibull distribution, conducts statistical analysis using the maximum likelihood estimation (MLE), Lindley’s approximation, and Markov Chain Monte Carlo (MCMC) algorithm to provide approximate estimates for the model. Finally, by comparing the results of numerical simulations, it is confirmed that the Bayesian estimation is more accurate and effective.

Transmuted Power Gumbel Distribution: Estimation and Applications

In recent years, generalized distributions have been widely studied in statistics as they possess flexibility in applications. This is justified because the traditional distributions often do not provide good fit in relation to the real data set studied. This paper develops a Power Gumbel distribution using the quadratic rank transmutation map (QRTM). The new generalization is called the transmuted Power-Gumbel distribution. Various mathematical properties of this distribution including moments, moment generating function, quantile function, mean deviation and order statistics were also studied. These features support the legitimacy and robustness of the proposed distribution. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators are assessed by simulation studies indicating that their precision improves with larger sample sizes. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. Finally, the usefulness of the proposed model is illustrated in an application to two real data sets and conclude that the four-parameter transmuted Power Gumbel distribution provides better fit than the other five models.

Toward Enhanced Geological Analysis: A Novel Approach Based on Transmuted Semicircular Distribution

This paper introduces a novel semicircular distribution obtained by applying the quadratic rank transmutation map to the stereographic semicircular exponential distribution, referred to as the transmuted stereographic semicircular exponential distribution (TSSCED). This newly proposed distribution exhibits enhanced flexibility compared to the baseline stereographic semicircular exponential distribution (SSCEXP). We conduct a comprehensive analysis of the model’s properties and demonstrate its efficacy in data modeling through the application to a real dataset.

Three Parameter Transmuted Exponential Distribution

Many distribution functions, can be explored in numerous dimensions with their extended form. In this paper an extended form of exponential distribution is studied by the quadratic rank transmutation map, called three parameter transmuted exponential distribution, where the base distribution is exponential distribution with two parameters \(\theta\) > 0 and \(\beta\) > 0 , shape and location parameters respectively. Some statistical properties have been studied for the said distribution including moments, quantile function, moment generating function, reliability analysis, mills ratio, reverse hazard rate function, order statistics, Bonferroni and Lorenz curves and indices, mean deviation about mean and median, estimation of parameter. The applicability have been explored by comparing value of -2ℓ, AIC and BIC using real data set.

A new generalized transmuted distribution

Abstract We introduced Transmuted another Two-Parameter Sujatha Distribution by using Quadratic Rank Transmutation Map technique. Various necessary statistical properties of Transmuted another Two-Parameter Sujatha Distribution are obtained. The reliability measures of proposed model are also derived and model parameters are estimated by using maximum likelihood estimation method. The significance of transmuted parameter has been tested by using likelihood ratio statistic. Finally, an application to real data sets is presented to examine the significance of newly introduced model by computing Kolmogorov statistic, p-value, AIC, BIC, AICC, HQIC.

A novel transmuted lomax exponential distribution: Properties and applications

Statistical lifetime distributions play a very important role in modeling data sets in various fields. Extending the existing distributions is of great interest in statistical research. The modification of the distributions provides more flexible model as compared to existing one. In this article, we propose a new probability model using Quadratic Rank Transmutation Map technique, named as Transmuted Lomax Exponential Distribution (TLED). The new distribution can model data sets with increasing, decreasing and bathtub shape hazard rates. Various statistical properties of the proposed distribution such as moments, order statistics, quantile function, mean residual life function and characteristic function are derived. Further, the parameter estimates are obtained through Maximum Likelihood method along with asymptotic confidence intervals. The utility of the new model is evaluated by analyzing two real data sets. In order to access the performance of the new model, several goodness of fit measures is used. The results indicate that the new model best fits the data as compared to the other extensions of the Lomax distribution.

The Transmuted Marshall-Olkin Extended Topp-Leone Distribution

In this paper, we introduced an extension of the Marshall-Olkin Extended Topp-Leone distribution using the quadratic rank transmutation map (QRTM). Statistical properties of the proposed distribution are examined and its parameter estimates are obtained using the maximum likelihood method. A real data set defined on a unit interval is employed to illustrate the usefulness of the proposed distribution among existing distributions with bounded support.

Acceptance sampling plans for the three-parameter inverted Topp-Leone model.

The quadratic rank transmutation map is used in this article to suggest a novel extension of the power inverted Topp-Leone distribution. The newly generated distribution is known as the transmuted power inverted Topp-Leone (TPITL) distribution. The power inverted Topp-Leone and the inverted Topp-Leone are included in the recommended distribution as specific models. Aspects of the offered model, including the quantile function, moments and incomplete moments, stochastic ordering, and various uncertainty measures, are all discussed. Plans for acceptance sampling are created for the TPITL model with the assumption that the life test will end at a specific time. The median lifetime of the TPITL distribution with the chosen variables is the truncation time. The smallest sample size is required to obtain the stated life test under a certain consumer's risk. Five conventional estimation techniques, including maximum likelihood, least squares, weighted least squares, maximum product of spacing, and Cramer-von Mises, are used to assess the characteristics of TPITL distribution. A rigorous Monte Carlo simulation study is used to evaluate the effectiveness of these estimators. To determine how well the most recent model handled data modeling, we tested it on a range of datasets. The simulation results demonstrated that, in most cases, the maximum likelihood estimates had the smallest mean squared errors among all other estimates. In some cases, the Cramer-von Mises estimates performed better than others. Finally, we observed that precision measures decrease for all estimation techniques when the sample size increases, indicating that all estimation approaches are consistent. Through two real data analyses, the suggested model's validity and adaptability are contrasted with those of other models, including the power inverted Topp-Leone, log-normal, Weibull, generalized exponential, generalized inverse exponential, inverse Weibull, inverse gamma, and extended inverse exponential distributions.

Generalized Rank Mapped Transmuted Distributions with Properties and Application: A Review

Generalizing probability distributions is a very common practice in the theory of statistics. Researchers have proposed several generalized classes of distributions which are very flexible and convenient to study various statistical properties of the distribution and its ability to fit the real-life data. Several methods are available in the literature to generalize new family of distributions. The Quadratic Rank Transmutation Map (QRTM) is a tool for the construction of new families of non-Gaussian distributions and to modulate a given base distribution for modifying the moments like the skewness and kurtosis with the ability to explore its tail properties and improve the adequacy of the distribution. Recently, a new family of transmutation map, defined as Cubic Rank Transmutation (CRT) has been used by several authors to develop new distributions with application to real-life data. In this article, we have done a review work on the existing generalized rank mapped transmuted probability distributions, available in the literature with various statistical properties such as the reliability, hazard rate and cumulative hazard functions, moments, mean, variance, moment-generating function, order statistics, generalized entropy and quantile function along with its applications. Some future works have also been discussed for generalized rank mapped transmuted distributions.

Transmuted Sushila Distribution and its application to lifetime data

The Sushila distribution is generalized in this article using the quadratic rank transmutation map as developed by Shaw and Buckley (2007). The newly developed distribution is called the Transmuted Sushila distribution (TSD). Various mathematical properties of the distribution are obtained. Real lifetime data is used to compare the performance of the new distribution with other related distributions. The results shown by the new distribution perform creditably well.

Transmuted esscher transformed laplace distribution and its application to microarray analysis

Esscher transformed Laplace distribution is a new class of asymmetric heavy tailed distribution. In this article, we generalize the Esscher transformed Laplace distribution using the quadratic rank transmutation map to develop transmuted Esscher transformed Laplace distribution. We derived the probability density function of transmuted Esscher transformed Laplace distribution and its various properties were studied. The maximum likelihood estimation procedure is employed to estimate the parameters of the proposed distribution and an algorithm in R package is developed to carry out the estimation. Simulation studies for various choices of parameter values were performed to validate the algorithm. Finally, we fitted the transmuted Esscher transformed Laplace, Esscher transformed Laplace and Gaussian distributions to microarray gene expression dataset and compared them.

A New Generalized Cauchy Distribution with an Application to Annual One Day Maximum Rainfall Data

In this article, we introduce a new three-parameter transmuted Cauchy distribution using the quadratic rank transmutation map approach. Some mathematical properties of the proposed model are discussed. A simulation study is conducted using the method of maximum likelihood estimation to estimate the parameters of the proposed model. We used two real datasets and compare various statistics to show the fitting and versatility of the model.

Transmuted complementary exponential power distribution: properties and applications

In this study, we introduce a new lifetime distribution by using quadratic rank transmutation map. The some properties of this new distribution is provided. Furthermore, the parameters of this new distribution are estimated by the maximum likelihood method. The performances of the estimates are examined according to bias and mean squared errors (MSEs) criteria through a Monte Carlo simulation study. Finally, two applications with real data are presented to evaluate the fits of introduced distribution.

A weighted transmuted exponential distributions with environmental applications

In this paper, we introduce a new three-parameter distribution. It is based on the combination of a re-parametrization of a general family of distributions (known as the EGNB2 distribution) and the so-called quadratic rank transmutation map defined with the exponential distribution as baseline. We explore some mathematical properties of this distribution including the hazard rate function, moments, the moment generating function, the quantile function, various entropy measures and (reversed) residual life functions. A statistical study investigates estimation of the parameters using the method of maximum likelihood. The distribution along with other existing distributions are fitted to two environmental data sets and its superior performance is assessed by using some goodness-of-fit tests. As a result, some environmental measures associated with these data are obtained such as the return level and mean deviation about this level.

THE TRANSMUTED HALF-NORMAL DISTRIBUTION WITH APPLICATION TO PRECIPITATION DATA

ABSTRACT The Half-Normal distribution has been intensively extended in the recent years. A review of the literature showed that at least 10 extensions of the Half-Normal distribution were introduced between 2008 and 2016. These extensions generalized the behavior of the density and hazard functions, which are restricted to monotonous decreasing and monotonically increasing, respectively. In this paper we propose a new extension called the transmuted Half-Normal distribution using the quadratic rank transmutation map, introduced by Shaw & Buckley (2009). A comprehensive account of mathematical properties of the new distribution is presented. We provide explicit expressions for the moments, moment-generating function, Shannon’s entropy, mean deviations, Bonferroni and Lorenz curves, order statistics, and reliability. The estimation of the parameters is implemented by the maximum likelihood method. The bias and accuracy of the estimators are assayed by the Monte Carlo simulations. This proposed distribution allows us to incorporate covariates directly in the mean and consequently to quantify their influences on the average of the response variable. Experiment with two real data sets show usefulness and its value as a good alternative to several extensions of the Half-Normal distribution in data modeling with and without covariates.

The Transmuted Marshall-Olkin Extended Lomax Distribution.

The transmuted family of distributions has been receiving increased attention over the last few years. In this paper, we generalize the Marshall-Olkin extended Lomax distribution using the quadratic rank transmutation map to obtain the transmuted Marshall-Olkin extended Lomax distribution. Several properties of the new distribution are discussed including the hazard rate function, ordinary and incomplete moments, characteristic function and order statistics. We provide an estimation procedure by the maximum likelihood method and a simulation study to assess the performance of the new distribution. We prove empirically the flexibility of the new model by means of an application to a real data set. It is superior to other three and four parameter lifetime distributions.

ON THE PROPERTIES AND APPLICATIONS OF A TRANSMUTED WEIBULL-RAYLEIGH DISTRIBUTION

This article presents a comprehensive study of the transmuted Weibull-Rayleigh distribution introduced by Yahaya and Ieren (2017) using Quadratic Rank Transmutation Map proposed by Shaw and Buckley (2007). The study comprises existing and new Mathematical and Statistical properties of the transmuted Weibull-Rayleigh distribution as contained in Yahaya and Ieren (2017). Most importantly, this paper unlike the first has considered two real life datasets to check for the performance of the transmuted Weibull-Rayleigh distribution and which the outcome indicates that the introduction of the transmuted parameter has added greater skewness and flexibility to the original Weibull-Rayleigh distribution which made it to fit the two datasets better than the Weibull-Rayleigh distribution and even the conventional Rayleigh distribution.

On the Properties and Applications of a Transmuted Lindley-Exponential Distribution

The Quadratic rank transmutation map proposed for introducing skewness and flexibility into probability models with a single parameter known as the transmuted parameter has been used by several authors and is proven to be useful. This article uses this method to add flexibility to the Lindley-Exponential distribution which results to a new continuous distribution called “transmuted Lindley-Exponential distribution”. This paper presents the definition, validation, properties, application and estimation of unknown parameters of the transmuted Lindley-Exponential distribution using the method of maximum likelihood estimation. The new distribution has been applied to a real life dataset on the survival times (in days) of 72 guinea pigs and the result gives good evidence that the transmuted Lindley-Exponential distribution is better than the Lindley-Exponential distribution, Exponential distribution and Lindley distribution based on the dataset used.

A transmuted version of the generalized half-normal distribution

An extension of the generalized half-normal distribution, given by Cooray and Ananda [5], is proposed and studied. We use the quadratic rank transmutation map to generate a transmuted version of the generalized half-normal distribution. We study some probability properties, discuss maximum likelihood estimation and present real data application indicating that the new distribution can improve the generalized half-normal distribution in fitting real data.

On the Performance of Transmuted Logistic Distribution: Statistical Properties and Application

In this article we transmute the logistic distribution using quadratic rank transmutation map to develop a transmuted logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its parent model to enhance more flexibility in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. The mathematical properties such as moment generating function, quantile, median and characteristic function of this distribution are discussed. The probability density functions of the minimum and maximum order statistics of the transmuted logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density function of the transmuted logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the transmuted logistic distribution performs better than its parent model.