Statisticians have created and proposed new families of distribution by extending or generalizing existing distributions. These families of distributions are made more flexible in fitting different types of data by adding one or more parameters to the baseline distributions. In this article, we present a new family of distributions called Type II half-logistic exponentiated-G family of distributions. We discuss some of the statistical properties of the proposed family such as explicit expressions for the quantile function, probability weighted moments, moments, generating function, survival and order statistics. The new family’s sub-models were discussed. We discuss the estimation of the model parameters by maximum likelihood. Two real data sets were employed to show the usefulness and flexibility of the new family
Order statistics are among the most fundamental tools in non-parametric statistics and inference. Special important cases of the order statistics are the minimum and maximum value of a sample, sample median and other sample quantiles. On this note, we obtained the r th minimum and maximum order statistic for the five parameter type II generalized logistic distribution using the probability distribution function and cumulative density function to obtain another five parameter type II generalized logistic distribution which shares the same properties by replacing p with np. We also obtain the quantile function by inverting the cumulative density function of the distribution which can be used to generate random samples arising from the distribution. The survival and hazard functions of the distribution are also obtained.
Population distributionof Pycnanthus. angolensis was carried out in two locations of three States (Osun, Ekiti and Oyo) due to abundance and availability using direct enumeration. A total of 58 stands of plant viz Osun state 58.93%, Ekiti State 28.57% and Oyo State 12.50% were assessed. Variation occurred within each State (Osun State: Ila 32.35% >20.59% Olooyo and Mojapa, Gbongan 17.65%, Ile Ogbo 5.88% and least in Ajaba (2.94%). In Ekiti State, Osan 43.75% > Otun 31.25%. > 25% Ayetoro Ekiti. In Oyo State, Adewumi, 28.57% > 14.29 %> Idito, Erumu, Sapara (U.I), Mosque (U.I) and Amina (U.I), 39 juvenile and 19 mature trees (flowering and fruiting) varied in ratios 30:6 Osun State, 9:7 Ekiti State and 0:6 Oyo state respectively. Osun State had the highest number of juvenile trees (30), 9 in Ekiti State and zero juvenile in Oyo state. Ekiti State had the highest number of mature tree 7> Oyo and Osun (6). Osun State had greater number of juvenile trees than Ekiti and Oyo States. P. angolensis was found growing in fallow or abandoned land, marshy areas, farmland, river side, new site areas and Quarters. P. angolensis could be found on different habitats among the States and within the States. Given the high rate of forest destruction in the country, there is need to ensure sustainable conservation of the forest area to avoid further destruction by provision of alternative means of livelihood for the local population so as to reduce their dependence on these forest.
In this study, a new four-parameter lifetime distribution called the Topp Leone KumaraswamyWeibull distribution was derived using the Topp-Leone Kumaraswamy-G family of distributions. The model includes several important sub-models as special cases such as Topp-Leone exponentiatedWeibull,Topp Leone Weibull, exponentiatedWeibull and Weibull distributions. An expansion for the probability distribution function was carried out which was used to derive some of the mathematical properties. Some mathematical properties of the distribution were presented such as moments, moment generating function, quantile function, survival function, hazard function as well as mean, 1st quartile, median and 3rd quartile. The probability distribution function of order statistics of the Topp-Leone KumaraswamyWeibull distribution was obtained. Estimation of the parameters by maximum likelihood estimation method was discussed. Two real-life application of the distribution was presented and the analysis showed the fit and flexibility of the new distribution over some lifetime models considered. The analysis showed that the model is effective in fitting biomedical data.
This paper is a further study of the five parameter type I generalized half logistic distribution. We derived some properties of the distribution. Estimation of the parameters of the distribution under complete observation was studied using the maximum likelihood method. To assess the flexibility of the distribution, it was applied to a real lifetime data and the results when compared to the sub-models showed that the five parameter type I generalized half logistic distribution performed best.
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