This study presents a four-parameter distribution which is called the Harris generalized Kappa distribution, which is flexible and tractable. The new distribution extends the two-parameter Kappa distribution, and it can be explored to model highly skewed data, especially those exhibiting decreasing, increasing, reversed J, and non-monotone (bathtub) failure rates. Mathematical expressions were derived for the statistical properties of the Harris generalized Kappa distribution and studied in detail, namely: moments, incomplete moments, moment generating functions, characteristic function, mean residual life, average waiting time, Bonferroni and Lorenz curves, Gini index, Renyi and q-entropies, and stress-strength reliability function. The estimate of the parameters of the proposed model is obtained using the maximum likelihood estimation procedure with the adequacy model in R. The application of the Harris generalized Kappa model to two lifetime data sets, namely the taxes revenue's data and the fracture toughness data sets, demonstrated its applicability in modeling real-life data, as it provides the best fit among other competitive models considered in the study.

We propose and develop the four-parameter Harris Extended Fréchet distribution. It is obtained by inserting the two-parameter Frechet distribution as the baseline in the Harris family and may be a useful alternative method to model income distribution and could be applied to other areas. We demonstrate that the new distribution can have decreasing, increasing and upside-down-bathtub hazard functions and that its probability density function is an infinite linear combination of Frechet densities. Some standard mathematical properties of the proposed distribution are derived, such as the quantile function, ordinary and incomplete moments, incomplete moments, Lorenz and Bonferroni curves, Gini index, Renyi and ????-entropies, mean residual life and mean inactivity time, probability weighted moments, stress-strength reliability, and order statistics. We also obtain the maximum likelihood estimators of the model. The potentiality/flexibility of the new distribution is illustrated by means two applications to failure and waiting time data sets

This article introduced a three-parameter extension of the Generalized Rayleigh distribution called half-logistic Generalized Rayleigh distribution, which has submodels the Generalized Rayleigh and Rayleigh distribution. The proposed model is quite flexible and adaptable to model any kind of life-time data. Its probability density function may sometimes be unimodal and its corresponding hazard rate may be of monotone or non-monotone shape. Standard statistical properties such as it ordinary and incomplete moments, quantile function, moment generating function, reliability function, stochastic ordering, order statistics, Renyi, and δ -entropy are obtained. The maximum likelihood method is used to obtain the estimates of the model parameters. Two practical examples of hydrological data sets are presented.

In this study, we developed a novel distribution called Gamma Inverse Exponential (GIE) distribution, which has proved to be a more flexible distribution in modeling COVID-19 case fatality in Nigeria. We studied some statistical properties of the new distribution, which include: moments, incomplete moments, quantile function, Renyi entropy, and mean deviation. A real-life data application to a number of reported cases of COVID-19 infection between March 2019 to 2021 shows that the GIE distribution has a better fit than some competing distributions in fitting the data. Time series analysis of the COVID-19 data is also considered.

In this paper, a new four-parameter distribution is developed and studied using the tractability properties of the Kumaraswamy generalized family of distributions and the features of the Inverse Lomax distribution. The newly developed distribution is called the Kumaraswamy Generalized Inverse Lomax distribution. We derive its main probability and reliability functions and examine its modeling behavior by considering different parameter combinations. Expectedly, the corresponding hazard rate function is very flexible; it possesses increasing, decreasing, and inverted (upside-down) bathtub shapes. Some important characteristics of the Kumaraswamy Generalized Inverse Lomax distribution are derived, including moments, incomplete moments, stress-strength reliability, probability weighted moments, Renyi and Tsallis entropy measures, order statistics, moment generating function, mean residual life, and mean activity time. The maximum likelihood estimation technique is used to obtain an estimate of the parameters of the new model, and a brief simulation study shows its effectiveness. The application of the new model is based on three real-life data sets used to show the modeling potential of the proposed distribution. The Kumaraswamy Generalized Inverse Lomax distribution turns out to be best by capturing important details in the structure of the data considered.

In this work, we present a four-parameter lifetime model that can be used to model reliability issues, fatigue life studies, and survival data called the Type II Topp-Leone Inverse Power Lomax distribution. It has the Type II inverse Lomax, Inverse Power Lomax, and Inverse Lomax distributions as sub-models. Some of its statistical properties, including complete and incomplete moments, generating functions, characteristics functions, mean residual life, mean inactivity time, Renyi entropy, Tsallis entropy, order statistics, stress-strength reliability, and weighted probability moment, have formal formulas that we have developed. The model's parameters are estimated using the maximum likelihood estimation technique. The effectiveness of maximum likelihood estimators is evaluated in terms of absolute bias and simulation study standard error. Two lifetime data sets are used to demonstrate how the new model can be applied. Using the same comparative criteria, the proposed distribution offers a better fit than a few well-known distributions.

This work introduces a new three-parameter modified extended inverted Weibull (MEIW) distribution which is a hybrid of the one-parameter inverted Weibull distribution. The density function of the MEIW can be expressed as a linear combination of the inverted Weibull densities. Some mathematical properties of the proposed MEIW model such as ordinary and incomplete moments, mean residual life, and mean waiting time, Tsallis entropy, moment generating function and order statistics are investigated. The maximum likelihood estimation method is considered to estimate the parameters of the MEIW model. The relevance of the MEIW model is studied via an application to neck cancer data.

In this work, we present a three-parameter lifetime model named Type-II Topp-Leone Bur XII distribution developed using the Type-II ToppLeone (TIITL-G) family of distributions proposed by Elgarhy et al. (2018) which can be used to model reliability problems, fatigue life studies, and survival data has been studied. The newly developed model is more flexible and can be used to model data of various shapes of the hazard function. We derived explicit expressions for some of its statistical properties such as ordinary moments, generating function, incomplete moments, mean deviation, Bonferroni and Lorenz curve, Renyi entropy, Tsallis Entropy, order statistics, and stochastic ordering. The maximum likelihood estimation technique is used to estimate the parameters of the model. The performance of maximum likelihood estimators is assessed in terms of absolute bias, and standard error of simulation study. The applicability of the new model is illustrated by using two lifetimes’ data sets. The proposed distribution provides a reasonable better fit than some well-known distributions using the same criteria of comparison.

We proposed and studied a flexible distribution with wider applications called Generalized Burr X Lomax (GBX-L) distribution. Some well-known mathematical properties such as ordinary moments, incomplete moment probability weighted moments, stress-strength model, mean residual lifetime, characteristic function, quantile function, order statistics and Renyi entropy of GBX-L distribution are investigated. The expressions of order statistics are derived. Parameters of the derived distribution are obtained using the maximum likelihood method and simulation studied is carried out to examine the validity of the method of estimation. The applicability of the proposed distribution is exemplified using aircraft data.

A new generalization of the Frechet distribution called Lehmann Type II Frechet Poisson distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, Renyi entropy, stochastic ordering, Bonferroni and Lorenz curve, mean and median deviation, stress-strength parameter are investigated. The maximum likelihood method is used to estimate the model parameters. We examine the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling three real data sets to illustrate empirically its flexibility and tractability in modeling life time data.

In this work, we present a five-parameter life time distribution called Harris power Lomax (HPL)  distribution which is obtained by convoluting the Harris-G distribution and the Power Lomax distribution. When compared to the existing distributions, the new distribution exhibits a very flexible probability functions; which may be increasing, decreasing, J, and reversed J shapes been observed for the probability density and hazard rate functions. The structural properties of the new distribution are studied in detail which includes: moments, incomplete moment, Renyl entropy, order statistics, Bonferroni curve, and Lorenz curve etc. The HPL  distribution parameters are estimated by using the method of maximum likelihood. Monte Carlo simulation was carried out to investigate the performance of MLEs. Aircraft wind shield data and Glass fibre data applications demonstrate the applicability of the proposed model.

This paper presents a new generalization of the extended Bur II distribution. We redefined the Bur II distribution using the Alpha Power Transformation (APT) to obtain a new distribution called the Alpha Power Transformed Extended Bur II distribution. We derived several mathematical properties for the new model which includes moments, moment generating function, order statistics, entropy etc. and used a maximum likelihood estimation method to obtain the parameters of the distribution. Two real-world data sets were used for applications in order to illustrate the usefulness of the new distribution.

In this work, we proposed and studied the Cubic Transmuted Gompertz (CTG) distribution using the Cubic Transmuted family of distributions which was introduced by Rahman et al. [8] and based on cubic transmutation map. We studied the statistical properties of the new distribution which includes: rth moment, moment generating function order statistics, mean, variance, Renyl entropy. The CTG distribution was fitted to a real data set to demonstrate its flexibility and tractability in modelling real life data.

This paper introduces a new extension of the Inverse Exponential distribution using the framework of Marshall-Olkin (1997) family of distributions. The new model is capable of modeling various shapes of aging and failure criteria. The statistical properties of the new model are discussed and the maximum likelihood and maximum product spacing’s methods are used to estimate the parameters involved. Explicit expressions are derived for the moments and the order statistics are examined for the new proposed model. Finally, the usefulness of the new model for modeling reliability data is illustrated using two real data sets with simulation study. Keywords: Inverse Exponential distribution, reliability analysis, maximum likelihood estimation, maximum product spacing’s estimates.

In this paper, we proposed a new four-parameter Extended Gumbel type-2 distribution which can further be split into the Lehman type I and type II Gumbel type-2 distribution by using a generalized exponentiated G distribution. The distributional properties of the proposed distribution have been studied. We derive the p th moment; thus, we generalize some results in the literature. Expressions for the density, moment-generating function, and r th moment of the order statistics are also obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix of the developed distribution. Two life data, which consist of data on cancer remission times and survival times of pigs, were used to show the applicability of the Extended Gumbel type-2 distribution in modelling real life data, and we found out that the new model is more flexible than its submodels.

This work provides a new statistical distribution named Cubic rank transmuted Inverse Weibull distribution which was developed using the cubic transmutation map. Various statistical properties of the new distribution which includes: hazard function, moments, moment generating function, skewness, kurtosis, Renyl entropy and the order statistics were studied. A maximum likelihood estimation method was used in estimating the parameters of the distribution. Applications to real data set show the tractability of the distribution over other distributions and its sub-model.

The convolution of Nadarajah-Haghighi-G family of distributions will result into a more flexible distribution (Nadarajah-Haghighi Gompertz distribution) than each of them individually in terms of the estimate of the characteristics in there parameters. The combination was done using Nadarajah-Haghighi (NH) generator. We investigated in the newly developed distribution some basic properties including moment, moment generating function, survival rate function, hazard rate function asymptotic behaviour and estimation of parameters. The proposed model is much more flexible and has a better representation of data than Gompertz distribution and some other model considered. A real data set was used to illustrate the applicability of the new model.

In this paper we introduced Gompertz Gumbel II (GG II) distribution which generalizes the Gumbel II distribution. The new distribution is a flexible exponential type distribution which can be used in modeling real life data with varying degree of asymmetry. Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which sometimes characterised the real life data. Structural properties of the new distribution namely, density function, hazard function, moments, quantile function, moment generating function, orders statistics, Stochastic Ordering, Renyi entropy were obtained. For the main formulas related to our model, we present numerical studies that illustrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the GGTT model. Three life data sets were used for applications in order to illustrate the flexibility of the new model.

In this work, we introduce a new generalization of the Inverted Weibull distribution called the alpha power Extended Inverted Weibull distribution using the alpha power transformation method. This approach adds an extra parameter to the baseline distribution. The statistical properties of this distribution including the mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and moment generating functions, reliability analysis, Lorenz and Bonferroni and curves, Rényi of entropy and order statistics are studied. We consider the method of maximum likelihood for estimating the model parameters and the observed information matrix is derived. Simulation method and three real life data sets are presented to demonstrate the effectiveness of the new model.

This work introduces a new generalization of the one parameter invertedWeibull distribution.The quadratic rank transmutation approach has been investigated.This new distribution is named exponentiated transmuted inverted Weibull (ETIW) distribution which is flexible and capable of modelling various shapes of ageing and failure characteristics.The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters.Explicit expressions were derived for the quantile, moment, and order statistics were examined.