The paper was to reduce biased Estimation using new approach (Penalized Maximum Likelihood Estimation (P(MLE)) method) in Logistic Regression. For this aim, unreal four small data sets were randomly generated. Maximum Likelihood Estimation ((MLE)) and P(MLE) methods were applied and compared for separation case including biased Estimation in Logistic Regression when one of the cells in 2 x 2 tables becomes equal to zero (separation problem). Parameters1 and their standard error obtained by using (MLE) for four data sets were 12.56±257.8, 13.46±264.3, 13.42±210.3, and 13.41±180.4, respectively, meaning that (MLE)’s are biased estimates. Corresponding values for P(MLE) method were found 2.28 ± 1.81, 3.05 ± 1.59, 3.45 ± 1.53, and 3.45 ± 1.53, respectively, meaning that P(MLE)’s was unbiased estimates. It is clear that standard error value for data set 1 reduced from 257.8 to 1.81 when using P(MLE) method for separation problem. According to P(MLE) method, the odds of being coronary heart disease risk for smokers were increased 21.08 times than that for non-smokers smoking in data set 2, which is significant at 1% level. The odds of being coronary heart disease risk for smokers were increased 31.63 times than that for non-smokers in data set 3 (P < 0.001). The odds of being coronary heart disease risk for smokers were increased 41.93 times than that for non-smokers in data set 4. When one of the cells in 2 x 2 contingency tables becomes equal to zero, P(MLE) was more superior to (MLE) method because P(MLE) method may be performed unbiased (reliable) Estimation.

Newton's method, which is also known as the Newton Raphson algorithm, as one of the most efficient numerical methods in mathematics, are known as a method and approach for the root approximation of nonlinear equations. After reviewing and interpretation of this method, one of the most widely used in the statistics, i. e. Estimation of the unknown parameters by Maximum Likelihood method is presented in this paper. To facilitate the transfer of concepts, the article includes several different numerical examples and computer programs.

In this research, the generalized Maximum Likelihood estimator (G(MLE)) is used to investigate the parameters Estimation for weighted distributions. There exist situations where the random sample from the population of interest is not available due to the data having unequal probabilities of entering the sample. The method of weighted distributions models the certainty of the probabilities of the events as observed and recorded. It is shown that if the mechanism of sample selection is known up to one unknown parameter, the Maximum Likelihood estimator ((MLE)) would be unidentifiable when the conjugate weight function is used. This problem is solved by addition of a prior distribution on model parameters yielding the G(MLE)s which are identifiable. We also propose the G(MLE)s for negative exponential, normal and Poisson weighted distributions when (MLE)s are unidentifiable.

Structural equation modeling (SEM) is a powerful multivariate statistical approach for assessing complex relationships between latent variables in many human and behavioral sciences. A common challenge in estimating structural equation models, which is based on hypothesis testing, is the presence of missing data. Deleting subjects with missing values on each of items is the usual way of handling missing data, which leads to biased estimators and lose a considerable amount of sample information as the percentage of missing values increases. In estimating SEM with missing values, one can apply the full information Maximum Likelihood (FIML) approach that makes maximal use of all available data from every subject in the sample. In this paper, the performance of FIML is investigated under three missing value mechanisms, missing completely at random, missing at random, and missing not at random, in a simulation study. Two confirmatory factor analysis models are considered, where the data is generated under three mechanisms and the impact of two indexes, sample size (100, 500) and percentage of missing values (2%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%), are evaluated based on the root mean square error of approximation (RMSEA) index. Results show that the performance of SEM using FIML approach is generally better than the performance of SEM without using this approach in terms of some goodness of fit index.

This study presents a Pseudo noise sequence (PN) Estimation algorithm using Maximum Likelihood method in low signal to noise ratio. The received signal samples are divided into temporal segments. Then correlation matrix is computed for eigenvalue Estimation. Eigenvector related to largest eigenvalue of this matrix is chosen and de-noised by stationary wavelet transform to find asynchronous of sequence and chip rate. The Estimation of PN sequence, is found through a Maximum Likelihood algorithm for delay Estimation and interpolation filter. Simulation results are applied to evaluate the proposed method and compare with previous methods in terms of computational complexity and accuracy of the chip rate and the PN Estimation. Furthermore, minimum number of required samples are investigated for true Estimation accuracy measurement. The results indicated that, the proposed method presented 13% better accuracy of PN sequence Estimation compared to other methods.

In this article, an attempt has been made to estimate the amount of sound transmission loss in a flat oval channel by applying the approach of statistical energy analysis. Correct Estimation of sound transmission loss in an air conditioning channel is of great importance due to the harmful effects of noise pollution in the environment on human health. Simulation with the statistical energy analysis method is a powerful approach to estimate sound and vibration in problems in which we deal with complex and multi-part systems; is considered. In this method, first, a system is divided into several subsystems, and then by writing a matrix equation that includes the energy exchanges between subsystems and energy loss coefficients; It is investigated from the perspective of vibration and sound Estimation.On average, the model presented in this research is able to estimate the sound transmission loss in different dimensions of the air conditioning channels according to the experimental results in the accuracy range of ± 2.5 dB. Considering that it seems that the results obtained from modeling with this method are in good agreement with the experimental data; The results of this research can be used as an efficient approach to estimate noise in oval shaped channels stretched in different lengths.