Abstract
In this work, a new three parameter distribution called the Inverse Weibull Rayleigh distribution is proposed. Some of its statistical properties were presented. The PDF plot of Inverse Weibull Rayleigh distribution showed that it is good for modeling positively skewed and symmetrical datasets. The plot of the hazard function showed that the proposed distribution can fit datasets with bathtub shape. Method of maximum likelihood estimation was employed to estimate the parameters of the distribution, the estimators of the parameters of Inverse Weibull Rayleigh distribution is asymptotically unbiased and asymptotically efficient from the result of the simulation carried out. Applying the new distribution to a positively skewed Vinyl Chloride data set shows that the distribution performs better than Rayleigh, Generalized Rayleigh, Weibull Rayleigh, Inverse Weibull, Inverse Weibull Weibull, Inverse Weibull Inverse Exponential and Inverse Weibull Pareto distribution in fitting the data as it has the smallest AIC value. Also, applying the new distribution to a negatively skewed bathtub shape failure rates data shows that the distribution is a competitive model after Weibull Rayleigh and Inverse Weibull Weibull distributions in fitting the data because it has the third least AIC value.
Highlights
Many researchers and statisticians nowadays are interested in generating families of distribution thereby creating a new distribution that will fit a data better
Applications In this subsection, we evaluated the fitness of the Inverse Weibull Rayleigh (IWR) distribution using two real data sets with other known distributions including Rayleigh, Generalized Rayleigh, Weibull Rayleigh, Inverse Weibull, Inverse Weibull Weibull, Inverse Weibull Inverse Exponential and Inverse Weibull Pareto distributions Data set 1: This represent 34 observations of the Vinyl Chloride dataobtained from clean up gradient ground-water monitoring wells in mg/L.The data are obtained from Bhaumiket al., (2009)
Application of eight competing distributions to data set two as shown in Table (8) shows that Inverse Weibull Rayleigh distribution performed third to Inverse Weibull Weibull distribution and Weibull Rayleigh distribution respectively, reason being that the data is negatively skewed
Summary
Many researchers and statisticians nowadays are interested in generating families of distribution thereby creating a new distribution that will fit a data better. Some popular known generating family are: The Beta-G by Eugene et al, (2002),Cordeiro and de Castro (2011) introduced Kumaraswammy generalized family, the Log-Gamma G family by Amini et al, (2014), Odd Frechet-G by Haq and Elgarhy (2018), Elbatal et al, (2018) proposed a new Alpha power transformation family of distributions, Hassan and Nassr (2018) introduced Inverse Weibull-G family among others. Hassan and Nassr (2018) added that Inverse Weibull distribution is an important distribution which can be used to analyze lifetime data.
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