in this paper we apply the homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of sturm-liouville type on $[0,pi]$ with neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued sign-indefinite number of $c^{1}[0,pi]$ and $lambda$ is a real parameter.

Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is ...

For fitness preferential attachment random networks, we define the empirical degree and pair measure, which counts the number of vertices of a given degree and the number of edges with given fits, and the sample path empirical degree distribution. For the empirical degree and pair distribution for the fitness preferential attachment random networks, we find a large deviation upper bound. From t...

the square map is one of the functions used in cryptography. for instance, the square map is used in rabin encryption scheme, block cipher rc6 and stream cipher rabbit, in different forms. in this paper, we study statistical properties of the output of the square map as a vectorial boolean function. we obtain the joint probability distribution of arbitrary number of the upper and the lower bits...

b a c k g r o u n d & aim: multi-state models can help better understand the process of chronic diseases such as cancers.  these models  are influenced  by assumptions  like individual  homogeneity.  this study aimed to investigate the effect of lack of individual homogeneity  assumption  in multi-state models. methods & materials: to investigate the effect of lack of individual homogeneity ass...

in this paper, the geometric distribution is considered. the means, variances, and covariances of its order statistics are derived. the fisher information in any set of order statistics in any distribution can be represented as a sum of fisher information in at most two order statistics. it is shown that, for the geometric distribution, it can be further simplified to a sum of fisher informatio...

the empirical bayes estimators of treatment effects in a factorial experiment were derived and their asymptotic properties were explored. it was shown that they were asymptotically optimal and the estimator of the scale parameter had a limiting gamma distribution while the estimators of the factor effects had a limiting multivariate normal distribution. a bootstrap analysis was performed to ill...

This paper considers an Extended Generalized Half Logistic distribution. We derive some properties of this distribution and then we discuss estimation of the distribution parameters by the methods of moments, maximum likelihood and the new method of minimum spacing distance estimator based on complete data. Also, maximum likelihood equations for estimating the parameters based on Type-I and Typ...

In this paper, we investigatethe boundary value problem for differential pencils on the half-linewith a turning point. Using a fundamental system of solutions, wegive a asymptotic distribution of eigenvalues.