This paper considers a non-mixture cure model for right censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Comparing with Weibull and exponentiated exponential distributions, the non-mixture Fréchet distribution is shown to be the best in modeling a real data on allogeneic marrow HLA-matched donors and ECOG phase III clinical trial e1684 data.

In this paper a more flexible extension of the Fréchet distribution is introduced. The new distribution is defined by means of the stochastic representation as the quotient of two independent random variables, a Fréchet distribution and the power of a random variable with uniform distribution in the interval (0,1). We will call this new extension the Slash Fréchet distribution and one of its main characteristics is that its tails are heavier than the Fréchet distribution. The general density of this distribution and some basic properties are determined. Its moments, skewness coefficients and kurtosis are calculated. In addition, the estimation of the model parameters is obtained by the method of moments and maximum likelihood. Finally, two applications with real data are performed by fitting the new model and comparing it with the Fréchet distribution.

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].