On Extended Quadratic Hazard Rate Distribution: Development, Properties, Characterizations and Applications

In this paper, we propose a flexible extended quadratic hazard rate (EQHR) distribution with increasing, decreasing, bathtub and upside-down bathtub hazard rate function. The EQHR density is arc, right-skewed and symmetrical shaped. This distribution is also obtained from compounding mixture distributions. Stochastic orderings, descriptive measures on the basis of quantiles, order statistics and reliability measures are theoretically established. Characterizations of the EQHR distribution are studied via different techniques. Parameters of the EQHR distribution are estimated using the maximum likelihood method. Goodness of fit of this distribution through different methods is studied

Cubic Rank Transmuted Modified Burr III Pareto Distribution: Development, Properties, Characterizations and Applications

In this paper, a flexible lifetime distribution called Cubic rank transmuted modified Burr III-Pareto (CRTMBIII-P) is developed on the basis of the cubic ranking transmutation map. The density function of CRTMBIII-P is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as moments, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The CRTMBIII-P distribution is characterized via ratio of truncated moments. Parameters of the CRTMBIII-P distribution are estimated using maximum likelihood method. The simulation study for the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII-P distribution is carried out. The potentiality of CRTMBIII-P distribution is demonstrated via its application to the real data sets: tensile strength of carbon fibers and strengths of glass fibers. Goodness of fit of this distribution through different methods is studied

On the Generalized Log Burr III Distribution: Development, Properties, Characterizations and Applications

In this paper, we present a generalized log Burr III (GLBIII) distribution developed on the basis of a generalized log Pearson differential equation (GLPE). The density function of the GLBIII is exponential, arc, J, reverse-J, bimodal, left-skewed, right- skewed and symmetrical shaped. The hazard rate function of GLBIII distribution has various shapes such as constant, increasing, decreasing, increasing-decreasing, upside- down bathtub and modified bathtub. Descriptive measures such as quantile function, sub- models, ordinary moments, moments of order statistics, incomplete moments, reliability and uncertainty measures are theoretically established. The GLBIII distribution is characterized via different techniques. Parameters of the GLBIII distribution are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). Goodness of fit of this distribution through different methods is studied. The potentiality and usefulness of the GLBIII distribution is demonstrated via its applications to two real data sets

On the modified Burr XII-Power distribution: development, properties, characterizations and applications

In this paper, a flexible lifetime distribution with increasing, decreasing and bathtub hazard rate called the Modified Burr XII-Power (MBXII-Power) is developed on the basis of the T-X family technique. The density function of the MBXII-Power is arc, exponential, left-skewed, right-skewed, J, reverse-J and symmetrical shaped. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBXII-Power distribution is characterized via different techniques. Parameters of the MBXII-Power distribution are estimated using maximum likelihood method. The simulation study is performed on the basis of graphical results to see the performance of maximum likelihood estimates (MLEs) of the MBXII-Power distribution. The potentiality of the MBXII-Power distribution is demonstrated by its application to real data sets: survival times of pigs, survival times of patients and quarterly earnings

On the Burr XII-Power Cauchy Distribution: Properties and Applications

We propose a new four-parameter lifetime model with flexible hazard rate called the Burr XII Power Cauchy (BXII-PC) distribution. We derive the BXII-PC distribution via (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The new proposed distribution is flexible as it has famous sub-models such as Burr XII-half Cauchy, Lomax-power Cauchy, Lomax-half Cauchy, Log-logistic-power Cauchy, log-logistic-half Cauchy. The failure rate function for the BXII-PC distribution is flexible as it can accommodate various shapes such as the modified bathtub, inverted bathtub, increasing, decreasing; increasing-decreasing and decreasing-increasing-decreasing. Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXII-PC distribution, we establish various mathematical properties such as random number generator, moments, inequality measures, reliability measures and characterization. Six estimation methods are used to estimate the unknown parameters of the proposed distribution. We perform a simulation study on the basis of the graphical results to demonstrate the performance of the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling estimators of the parameters of the BXII-PC distribution. We consider an application to a real data set to prove empirically the potentiality of the proposed model

On the Burr XII-moment Exponential Distribution

In this study, a new flexible lifetime model called Burr XII moment exponential (BXII-ME) distribution is introduced. We derive some of its mathematical properties including the ordinary moments, conditional moments, reliability measures and characterizations. We employ different estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods for estimating the model parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators of the BXII-ME distribution. We verify the potentiality of the BXII-ME model via monthly actual taxes revenue and fatigue life applications

On Burr III Marshal Olkin Family: Development, Properties, Characterizations and Applications

In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of BIIIMO-G family is demonstrated by its application to real data sets

On Generalized Log Burr Xii Distribution

In this paper, we present flexible generalized log Burr XII (GLBXII) distribution developed on basis of generalized log Pearson differential equation. GLBXII distribution is also obtained from compounding mixture of distributions. Some structural and mathematical properties including moments, inequality measures, uncertainty measures and reliability measures are theoretically established. Characterizations of GLBXII distribution are studied through different techniques. Parameters of GLBXII distribution are estimated using maximum likelihood method. Goodness of fit of probability distribution through different methods is studied

ON THE NEW FAMILY OF KIES BURR XII DISTRIBUTION

We propose a new lifetime model derived from the T-X generator called the new family of Kies Burr XII (NFKBXII) distribution. The NFKBXII density function is symmetrical, right-skewed, left-skewed, J, reverse-J, U and exponential shaped. The NFKBXII model failure rates can be monotone and non-monotone in shapes depending on the selection of the parameters. To show the importance of the NFKBXII distribution, we establish various mathematical properties such as random number generator, moments, density functions of record values, reliability and characterizations. We address the maximum likelihood estimates (MLE) for the NFKBXII parameters. We estimate the precision of the maximum likelihood estimators via a simulation study. We consider an application to serum-reversal times to clarify the potentiality and utility of the NFKBXII model along with NKBXII, KMBXII, KBXII, NKL, KL, MBXII, MBIII, Weibull and inverse Weibull distributions. We apply goodness of fit statistics (GOFs), various model selection criteria, and graphical tools to examine the adequacy of the NFKBXII distribution

Cubic Rank Transmuted Modified Burr III Distribution: Development, Properties, Characterizations and Applications

We propose a lifetime distribution with flexible hazard rate called cubic rank transmuted modified Burr III (CRTMBIII) distribution. We develop the proposed distribution on the basis of the cubic ranking transmutation map. The density function of CRTMBIII is symmetrical, right-skewed, left-skewed, exponential, arc, J and bimodal shaped. The flexible hazard rate of the proposed model can accommodate almost all types of shapes such as unimodal, bimodal, arc, increasing, decreasing, decreasing-increasing-decreasing, inverted bathtub and modified bathtub. To show the importance of proposed model, we present mathematical properties such as moments, incomplete moments, inequality measures, residual life function and stress strength reliability measure. We characterize the CRTMBIII distribution via techniques. We address the maximum likelihood method for the model parameters. We evaluate the performance of the maximum likelihood estimates (MLEs) via simulation study. We establish empirically that the proposed model is suitable for strengths of glass fibers. We apply goodness of fit statistics and the graphical tools to examine the potentiality and utility of the CRTMBIII distribution