No abstract

In this paper, a new block method of the second order is presented to solve initial value problems numerically. This method is similar to the block trapezoidal rule [S. Abbas and L.M. Delves, Parallel solution of ODE's by one step block methods, Report CSMR, University of Liverpool, 1989.], where the low power of the block size appears in the principal local truncation error. Direct comparison with the related results of the block trapezoidal rule has been outlined.

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

The inverse Weibull distribution which was first introduced to investigate the decay of mechanical components is widely used in the field of biology, especially in the areas of survival and reliability analysis. In this paper, a generalisation of inverse Weibull distribution is presented using a new class of gamma distributions. For the proposed model, important mathematical properties including quantile function, noncentral moment, central moment, moment generating function, characteristics function, and general coefficient are discussed. The shapes of the probability density function and risk function were obtained and the graphical demonstrations of them were provided. To estimate model parameters of the proposed method, maximum likelihood was used. An illustrative simulation study was conducted to observe how the maximum likelihood estimators behave for different sample sizes and for different values of parameters. Two real data sets from the field of biomedical sciences were used to demonstrate the practical applications of the proposed model in real life phenomena. Results were obtained from the data sets, using the gamma inverse Weibull distribution and some known existing distributions and compared. The comparative analysis justified that the proposed model significantly fits with the survival data compared to other distributions.

In this article, a new three parameter lifetime model is proposed as a generalisation of the moment exponential distribution. The proposed model is named as Topp-Leone moment exponential distribution. The induction of two additional shape parameters will enhance the capability of the proposed model to handle the complex scenarios in modelling. Several properties of the proposed model are discussed. The model parameters are estimated using method of maximum likelihood. Real life applications of the proposed model have been carried out by using datasets from the fi elds of botany, archaeology and ecology.