Probability distributions and their generalisations have contributed greatly in the modeling and analysis of random variables. However, due to the increased introduction of new distributions there has been a major problem with choosing and applying the right distribution for a given set of data. In most cases, it is discovered that the data set in question fits two or more probability distributions and hence one must be chosen among others. The Lomax-Weibull and Lomax-Log-Logistic distributions introduced in an earlier study using a Lomax-based generator were found to be positively skewed and may be victims of this situation especially when modelling positively skewed datasets. In this article, we apply the two distributions to some selected datasets to compare their performance and provide useful insight on how to select the most fit among them when dealing with a real-life situation. We used the log-likelihood value, AIC, CAIC, BIC, HQIC, Cramér-Von Mises (W*) and Anderson Darling (A*) statistics as performance evaluation tools for selecting between the two distributions.

The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.

In this article, the Quadratic rank transmutation map proposed and studied by Shaw and Buckley [1] is used to construct and study a new distribution called the transmuted Lomax-Exponential distribution (TLED) as an extension of the Lomax-Exponential distribution recently proposed by Ieren and Kuhe [2]. Using the transmutation map, we defined the probability density function and cumulative distribution function of the transmuted Lomax-Exponential distribution. Some properties of the new distribution such as moments, moment generating function, characteristics function, quantile function, survival function, hazard function and order statistics are also studied. The estimation of the distributions’ parameters has been done using the method of maximum likelihood estimation. The performance of the proposed probability distribution is being tested in comparison with some other generalizations of Exponential distribution using a real life dataset. The results obtained show that the TLED performs better than the other probability distributions.

The Rayleigh was obtained from the amplitude of sound resulting from many important sources by Rayleigh. It is continuous probability distribution with a wide range of applications such as in life testing experiments, reliability analysis, applied statistics and clinical studies. However, it is not flexible enough for modeling heavily skewed datasets as compared to compound distributions. In this paper, we introduce a new extension of the Rayleigh distribution by using a Gompertz-G family of distributions. This paper defines and studies a three-parameter distribution called “Gompertz-Rayleigh distribution”. Some properties of the proposed distribution are derived and discussed comprehensively in this paper and the three parameters are estimated using the method of maximum likelihood estimation. The goodness-of-fit of the proposed distribution is also evaluated by fitting it in comparison with some other existing distributions using a real life data.

The purpose of this paper is to find out the operating characteristics of the ATM service point of the Fidelity bank Plc, plateau state. Specifically, a computer package (MS60) was used for analyzing the data. Results obtained from the analysis showed the traffic intensity (ρ) to be 0.96, which indicated that the service facility is highly utilized. The average length of the queue was found to be 21 while the average waiting time in the queue was 1.10 hours. On the basis of this investigation, the conclusion was made that the service utility is highly utilized, implying that there are more customers than the service point can accommodate thus giving rise to the lengthy customer waiting time. It is recommended that one additional ATM be deployed to the bank's premises so as to minimize customer waiting time and to also increase the service rate.