A new edge-corrected estimator is proposed for the second moment cumulative function K(t) introduced by RIPLW (1977, JoumrJ of tlre Royal Slatiaticd Society, SetieS B 39, 172-212). This new estimator is compared by simulation methods with existing edge-corrected estimators in the context of both K ( t ) and L(t) functions which are used to study point patterm. The results of the simulation study suggests that the new estimator provides almost unbiased estimates of K ( t ) and L(t) and has a smaller mean squared error than ita predecessors.

We proposed a new family of distributions called the Topp Leone exponentiated-G family of distributions with two extra positive shape parameters, which generalizes and also extends the Topp Leone-G family of distributions. We derived some mathematical properties of the proposed family including explicit expressions for the quantile function, ordinary and incomplete moments, generating function and reliability. Some sub-models in the new family were discussed. The method of maximum likelihood was used to estimate the parameters of the sub-model. Further, the potentiality of the family was illustrated by fitting two real data sets to the mentioned sub-models.

We proposed a new class of distributions with two additional positive parameters called the Inverse Lomax-G (IL-G) class. A special case was discussed, by taking Weibull as a baseline. Different properties of the new family that hold for any type of baseline model are derived including moments, moment generating function, entropy for Renyi, entropy for Shanon, and order statistics. The performances of the maximum likelihood estimates of the parameters of the sub-model of the Inverse Lomax-G family were evaluated through a simulation study. Application of the sub-model to the Breaking strength data clearly showed its superiority overthe other competing models.

SumnulryEdge-corrected kernel-baeed estimators are proposed for the pair-correlation function g(t). These estimators are compared by simulation methods with the existing edge-corrected estimator SUggated by FIKSEL (1988, Statistics, 19, 67-75). The results of the simulation st.udy suggests that all the edge-corrected estimators ale almost unbiased. Furthermore, the estimators proposed in this paper have a smaller mean squared error than the existing alternative. Finally, the catoptrophorus semipalmatus nesting pattern is explored.

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