This study proposed an Exponential Chen Inverse Rayleigh (ECIR) distribution to the tackle the difficulties of modeling failure rates that exhibit both monotonic and non-monotonic behavior, as well as appropriately capturing the bathtub curve in reliability engineering. The properties of the ECIR distribution like the survival function, hazard function, cumulative Hazard function, moments and ordered statistics were derived. The simulation result for median, skewness, and kurtosis of ECIRD (β,λ,δ,φ) with different parameter values of β,λ, δ and φ result indicated that the distributions are right-skew, with peakness and tail behavior similar to that of a normal distribution, albeit with some variations. Findings from the application of ECIRD to the survival times (in days) for 72 guinea pigs infected with virulent tubercle bacilli, revealed that ECIR model emerge as the most preferred among the competing models. The ECIR model exhibits the best overall performance, with the lowest values for -2LL which confirms that it provides the most parsimonious fit to the data. The proposed ECIR model also exhibited standard errors that suggest variability in the estimates. Read more

This paper presents a mixture distribution of a new modelling tool,which is termed Gumbel-Exponential (GEXP) distribution. The distribution allows us to capture some real characteristics of data and it is an important tool for understanding the phenomenon. The various statistical properties of this distribution were fully explored and discussed, these include; the mean, variance, moments, mode, reliability function and hazard function.The worth of the mixing distribution has been demonstrated by applying it to real life data. Read more

The paper projects innovating means to probability modeling using integration method and the concept of normalization. It brings to light a probability distribution obtained by combining a probability density function of a distribution and a cumulative distribution function of another continuous probability model, to produce a triangular trend and a half bell-curve trend. Gumbel and exponential distributions are the root-distributions used for this development. The properties of the distribution include moments and related measures, and estimation, studied alongside simulation. Read more

The process of introducing extra parameters or mathematical constants into existing distribution to increase its flexibility and performance has yielded good results in the area of statistical theory and applications. The trigonometric based Sine-G family, a method of developing new distributions, is one of the most efficient methods proposed and studied for introducing skewness and flexibility into probability distributions. In this paper, the method has been used to add flexibility to the Lomax-exponential distribution resulting to a new continuous distribution known as “Sine Lomax-Exponential distribution”. The properties, estimation of parameters and simulation study of the new distribution using the method of maximum likelihood estimation with real life applications are presented and discussed in this paper. The new model has been applied to two survival datasets and the result is being compared among the fitted distributions using some information criteria. Read more

The design of the queueing model involves modelling the arrival and service processes of the system. Conventionally, the arrival process is assumed to follow Poisson while service times are assumed to be exponentially distributed. Other distributions such as Weibull, uniform, lognormal have been used to model service times however, generalized distributions have not been used in this regard. In recent times, attention have been shifted to generalised families of distributions including Beta generalized family of distributions which led to the development of Beta-based distributions. Distributions generated from a mixture of beta random variables are quite numerous in literature with little or no application to service times data. In this study, six Beta-based compound distributions namely; Beta-Log-logistic distribution (BLlogD), Beta-Weibull distribution (BWeiD), Beta-Lomax distribution (BLomD), Beta-exponential distribution (BExD), Beta-Gompertz distribution (BGomD) and Beta-log-normal distribution (BLnormD)) were compared with the classical service times model on four service times data sets. Maximum likelihood estimator was employed in estimating parameters of the selected models while Akaike Information Criteria (AIC), Consistent Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC) and Hannan Quin information criterion (HQIC) statistics were employed to select the best model. CDFs, PDFs and PP-plots were used to fit the data of the suggested models. Results from the study shows that Beta-Exponential distribution (BExpD) performed better for the datasets I (AIC=640.3, CAIC=640.5,BIC=648.1 and HQIC=643.4), Beta-weibull distribution (BWeiD) performed better for the data sets II and III (AIC=204.2, 2142.4,CAIC=204.2, 2142.7,BIC=212.8, 2154.9 and HQIC=207.6, 2147.5) while Beta-log-logistic distribution (BLlogD) performed better for the data sets IV (AIC=2275.3,CAIC=2275.5, BIC=2289.3 and HQIC=2280.9). Findings from this study revealed some useful Beta-based compound distributions which performed better than the conventional service time model. From the findings of this study, we recommend researchers to dive deep into queueing theory. Read more

In statistical literature, various methods exist for developing new distributions. This paper introduces a new distribution derived using the GAYUF transformation. We explore several structural properties of this distribution, including moments, moment generating function, mean, variance, hazard rate and its shape, survival function, and more. The parameters of the newly developed distribution are estimated using the maximum likelihood estimation (MLE) method and validated through simulation studies. Additionally, we apply the distribution to two real-world datasets to demonstrate its practical applications. The findings suggest that the new distribution is a robust tool for modeling and analyzing data in engineering and other fields, providing enhanced fit and reliability for parameter estimation Keywords: Exponential Distribution, hazard function, statistical properties, maximum likelihood estimation (MLE) Read more

This paper focused on the use of three probability distributions to justify the central limit theorem (CLT). The aim was to use the moment generating function (MGF) to prove (CLT) and also to portray the shape of different sample sizes (15, 30 and 100) of distributions of sample means on a histogram. The population distributions studied were: Normal, Gamma and Exponential distributions. In addition, sampling distribution of the mean table was constructed for better understanding of CLT. The study used simulation to simulate population distribution of Normal, Gamma and Exponential. Five hundred (500) distributions of sample means were drawn from each of the simulated population distributions at three different sample sizes (n): 15, 30 and 100. The shape of the simulated population distribution and sampling distribution of mean were presented on a histogram. The mean and standard deviation of each population distribution together with distribution of sample means at different sample sizes were also presented on the histogram plotted. The findings showed that under normal distribution, the sampling distribution of mean produced a shape like normal distribution irrespective of the sample size. Conversely, the shape of sampling distribution of mean under non-normal distributions gradually converges to normal distribution as sample size tends to infinity, while the variability of each sampling distribution decreases as the sample size increases. Therefore, CLT holds for large sample size (n ≥ 30). Read more

The main aim of this study is to add to the existing literature on probability distributions. In this study, the transmutation map approach proposed by Shaw and Buckley (2007) was used to develop a probability distribution called Transmuted Topp-Leone Exponential (TTLE) distribution. The moment, moment generating function and entropy are among the statistical properties of the distribution that were derived. The maximum likelihood approach was used to estimate the parameters of the novel distribution. The TTLE distribution was applied to a real-world data set and compared to other well-known standard distributions; the result of the analysis revealed that the newly developed distribution is more superior than the competing models. Read more