J. Ohakwe

The Exponentiated Gumbel Type-2 Distribution: Properties and Application

We introduce a generalized version of the standard Gumble type-2 distribution. The new lifetime distribution is called the Exponentiated Gumbel (EG) type-2 distribution. The EG type-2 distribution has three nested submodels, namely, the Gumbel type-2 distribution, the Exponentiated Frechet (EF) distribution, and the Frechet distribution. Some statistical and reliability properties of the new distribution were given and the method of maximum likelihood estimates was proposed for estimating the model parameters. The usefulness and flexibility of the Exponentiated Gumbel (EG) type-2 distribution were illustrated with a real lifetime data set. Results based on the log-likelihood and information statistics values showed that the EG type-2 distribution provides a better fit to the data than the other competing distributions. Also, the consistency of the parameters of the new distribution was demonstrated through a simulation study. The EG type-2 distribution is therefore recommended for effective modelling of lifetime data.

Marshall-Olkin Generalized Erlang-truncated Exponential Distribution: Properties and Applications

This article introduces the Marshall–Olkin generalized Erlang-truncated exponential (MOGETE) distribution as a generalization of the Erlang-truncated exponential (ETE) distribution. The hazard rate of the new distribution could be increasing, decreasing or constant. Explicit-closed form mathematical expressions of some of the statistical and reliability properties of the new distribution were given and the method of maximum likelihood estimation was used to estimate the model parameters. The usefulness and flexibility of the new distribution was illustrated with two real and uncensored lifetime data-sets. The MOGETE distribution with a smaller goodness of fit statistics always emerged as a better candidate for the data-sets than the ETE, Exp Fréchet and Exp Burr XII distributions.

Transmuted Erlang-Truncated Exponential Distribution

Abstract This article introduces a new lifetime distribution called the transmuted Erlang-truncated exponential (TETE) distribution. This new distribution generalizes the two parameter Erlang-truncated exponential (ETE) distribution. Closed form expressions for some of its distributional and reliability properties are provided. The method of maximum likelihood estimation was proposed for estimating the parameters of the TETE distribution. The hazard rate function of the TETE distribution can be constant, increasing or decreasing depending on the value of the transmutation parameter Φ ⁢ [ - 1 , 1 ]

The adjusted Fisk Weibull distribution: properties and applications

{\Phi[-1,1]}

Forecasting Nigeria’s inflation and the world prices of her major agricultural export commodities with probability distributions via VaR and ES and estimating their dependence via copula

; this property makes it more reasonable for modelling complex lifetime data sets than the ETE distribution that exhibits only a constant hazard rate function. The goodness of fit of the TETE distribution in analyzing real life time data was investigated by comparing its fit with that provided by the ETE distribution and the results show that the TETE distribution is a better candidate for the data. The stability of the TETE distribution parameters was established through a simulation study.

The Extended Erlang-Truncated Exponential distribution: Properties and application to rainfall data

Abstract We define a new lifetime distribution from a direct cumulative distribution function composition of the two parameter Fisk distribution and two parameter Weibull distribution with an asymptotic adjustment. The new four parameter distribution is called the adjusted Fisk Weibull (AFW) distribution. The AFW distribution is analytically appealing and some of its statistical properties are expressed in closed forms. The maximum likelihood method of parameter estimation was used to estimate the parameters of the new distribution and the usefulness and possible applications of the distribution was illustrated with two real and uncensored data-sets.

The modified Power function distribution

ABSTRACT Eleven most common distributions in finance are fitted to the monthly log-returns of the average world prices of Nigeria’s major agricultural export commodities and inflation in Nigeria. After considerable model selection procedure; the logistic distribution is shown to give the best fit to the world prices data, while the generalized logistic distribution gives the best fit to the inflation data. Five most popular Archimedean copulas are used to describe the dependence between the two macroeconomic variables and the Clayton copula emerged as the best fitting copula. The emergence of the Clayton copula suggests a link between low world prices of Nigeria’s major agricultural export commodities and low inflation in Nigeria. The Kendall’s-tau dependence measure of the Clayton copula indicates about 12% dependency of Nigeria’s inflation on the world prices of her major agricultural export commodities. Forecasts based on Value at Risk and Expected Shortfall are given.

A Note on Modeling the Maxima of Lagos Rainfall

The Erlang-Truncated Exponential ETE distribution is modified and the new lifetime distribution is called the Extended Erlang-Truncated Exponential EETE distribution. Some statistical and reliability properties of the new distribution are given and the method of maximum likelihood estimate was proposed for estimating the model parameters. The usefulness and flexibility of the EETE distribution was illustrated with an uncensored data set and its fit was compared with that of the ETE and three other three-parameter distributions. Results based on the minimized log-likelihood (−ℓˆ), Akaike information criterion (AIC), Bayesian information criterion (BIC) and the generalized Cramér–von Mises W⋆ statistics shows that the EETE distribution provides a more reasonable fit than the one based on the other competing distributions.

A Note on a Comparison of Methods for the Estimation of Weibull Distribution Parameters of Nwobi and Ugomma

Recently, a lot of new, improved, flexible and robust probability distributions have been developed from the existing distributions to encourage their applications in diverse fields. This paper proposes a new lifetime distribution called the Modified Power function (MPF) distribution, the distribution belongs to the Marshall-Olkin-G family of distribution and it’s an extension of the one parameter Power function distribution. The MPF distribution enjoys a close form distributional expression. Some of its statistical properties including possible transformations are presented. The paper suggests the use of maximum likelihood method of parameter estimation for estimating the parameters of the new distribution. The applicability of the distribution was illustrated with two real data-sets and its goodness-of-fit was compared with that of the Exponential, Weibull, Lindley Exponential, Exponentiated Exponential, Kumaraswamy, Power function and Beta distributions by using the AIC, AICc, CAIC, BIC, HQC, and goodness-of-fit measures and the results shows that the MPF distribution is the best candidate for the data-sets.