Al-Hussaini and Ateya [3−4] obtained the maximum likelihood and Bayes estimates of the parameters, reliability function (rf) and hazard rate function (hrf) of a mixture of two components of truncated type I generalized logistic distribution, TTIGL(β, γ, α), with location parameter β, scale parameter γ and shape parameter α, when the location parameters are equal to zero, when the scale paramete...

we consider the coupled system$f(x,y)=g(x,y)=0$,where$$f(x, y)=bs 0 {m_1}   a_k(y)x^{m_1-k}mbox{ and } g(x, y)=bs 0 {m_2} b_k(y)x^{m_2-k}$$with entire functions $a_k(y), b_k(y)$.we    derive a priory estimates  for the sums of the rootsof the considered system andfor the counting function of  roots.

In this paper, rstly, we obtain some inequalities which estimates complex polynomials on the circles.Then, we use these estimates and a Moebius transformation to obtain the dual of this estimates forthe lines in upper half-plane. Finally, for an increasing weight on the upper half-plane withcertain properties and holomorphic functions f on the upper half-plane we obtain an equivalentrepresenta...

Determining how monetary policy makers react to changes in key economic variables has been of major interest to monetary economists. Estimates of monetary policy rules (reaction functions) are a widely used method for doing this. Behavior differs under different policy regimes, as in rule-based systems or chronic inflation. In practice, estimates of instrument rules have been used to descri...

We study holonomic gradient decent for maximum likelihood estimation of exponentialpolynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of the distribution is the set of positive reals. We show that the maximum likelihood estimate (MLE) can be easily computed by the holonomic gradient descent, even...

The purpose of this paper is to give an overview on the use of the Expectation-Maximization (EM) algorithm in software reliability modeling. This algorithm is related to Maximum Likelihood Estimates (MLE) of parameters in a context of missing data. Different ways to implement this algorithm are highlighted for hidden Markov models in software reliability.

In statistics, an expectationmaximization (EM) algorithm is an iterative method for finding maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated usin...

The Expectation/Conditional Maximisation Either (ECME) algorithm has proven to be an effective way of accelerating the Expectation Maximisation (EM) algorithm for many problems. Recognising the limitation of using prefixed acceleration subspaces in ECME, we propose a Dynamic ECME (DECME) algorithm which allows the acceleration subspaces to be chosen dynamically. The simplest DECME implementatio...

In many of the studies concerning Accelerated life testing (ALT), the log linear function between life and stress which is just a simple re-parameterization of the original parameter of the life distribution is used to obtain the estimates of original parameters but from the statistical point of view, it is preferable to work with the original parameters instead of developing inferences for the...