Likelihood Estimation Method Research Articles

Likelihood and Bayesian Estimation Methods for Poisson Process Models in Software Reliability

The contents and function of a computer package to fit reliability models for computer software are outlined. Parameters in the models are, in the first place, estimated by maximum likelihood estimation procedures. Bayesian estimation methods are also used and are shown to give estimates with a smaller variance than their MLE counterparts. An example of the application to a particular set of failure times is given.

刺激―反応データにおける順序カテゴリー間隔比例モデル

In this paper, we propose an individual-difference model based on the models by Samejima(1969)and Andrich(1978a), that can be effectively used in the analysis of ordered categorical responses. In this model each individual has his own values of the thresholds of categories with proportional intervals.The method of maximum likelihood estimation for the parameters in the model, using Fisher's scoring method, is presented. The advantage of the model is that it is possible to estimate the thresholds' parameters even when an individual has no responses for some cate gories. Finally, an example is presented, in which the model provides productive findings.

On Latent Distance Analysis and the MLE Algorithm

Latent distance analysis proposed by Lazarsfeld (1968) is discussed and the method of the maximum likelihood estimation (MLE) of the latent parameters is studied. For this problem, it is well-known that the ordinary algorithm of MLE gives frequently improper solutions. In the present paper, an algorithm is proposed, which does not give any improper solution, after transforming the latent response parameters to the logistic form and applying the new MLE procedure. The algorithm depends on the EM algorithm. The actual data analysis is also given.

On the method of maximum likelihood estimation for the log-Pearson type 3 distribution

On the method of maximum likelihood estimation for the log-Pearson type 3 distribution

Maximum likelihood methods of estimation for disequilibrium models in a centrally planned economy

Maximum likelihood methods of estimation for disequilibrium models in a centrally planned economy

Small sample comparison of Thompson’s estimator to some common bioassay estimators

For a variety of reasons, bioassay experiments are frequently conducted with small sample sizes. However, the statistical literature offers little comparative information for small sample sizes among the analytical procedures most typically applied in vertebrate studies for chemical registration. A simulation study was performed to compare several traditional analytical procedures for estimating the median lethal dose (LD50). These estimation procedures include probit analysis with maximum likelihood estimation, logit analysis with maximum likelihood and minimum chi-square estimation methods, and analysis by a nonparametric moving average procedure. The simulation results indicate the conditions under which each analytical method appears most useful. Recommendations are tentatively made for minimally adequate designs for bioassay studies.

The poisson-inverse gaussian disiribuiion as a model for species abundance

An inverse Gaussian mixture of Poisson distributions(the P-IG distribution) is considered as a model for species abundance data,, Minimum chi-square and maximum likelihood methods of estimation for the zero-truncated P-IG distribution are developed, Ihe performance of the P-IG distribution is illustrated and discussed for several well-known sets of insect abundance data.

Box-cox transformation and the problem of heteroscedasticity

It is known that heteroscedasticity in the context of the well-known family of power transformations suggested by Box and Cox creates complications because it depends upon the heteros- cedasticity of the original values of the dependent variable in a regression model set-up) as well as upon the transforma- tion parameter In this paper we attempt at generalizing the original Box-Cox model in this direction, and suggest maximum likelihood method of estimation for the parameters of the model. Through illustrative examples we show the seriousness of the problem of heteroscedasticity in the context of this trans- formation, and indicate how one can separate out the problem of non-linearity from the influence of stabilization of error variance in an estimate of the transformation parameter in our generalized model.

Effects of visitation frequency and instrument reliability on the accuracy of estimation of river discharges

ABSTRACT The process of failures of a gauging station can be modelled as Poisson with time to the first failure distributed exponentially. The process is restarted when the station is visited and serviced. The probability distributions of the number of failures and the length of the missing record associated with gauging-station failures are derived as functions of the average time to failure, τO, and the pattern and frequency of visits. A maximum likelihood method of estimation of τO from readily available data is proposed and analysed. This method gives estimates of τO which, for samples containing a reasonably large number of failures, are approximately unbiased, efficient and normally distributed. A moment method of estimation of τO is also proposed. Methods for validation of the assumed model and for testing the uniformity between stations or groups of stations are presented. The proposed methodology has been applied to study the performance of a network of 168 gauging stations.

Folded Equations for a Weibull Maximum Likelihood Ratio Test

An improved non-myopic method of maximum likelihood estimation for a 2-parameter Weibull model with multi-censored samples, is derived and demonstrated. Maximum likelihood ratio testing of two hypotheses is discussed for: 1) homogeneous shape parameters, and 2) a composite of homogeneous shape and scale parameters.

Bayesian estimation of the complete sample size from an incomplete poisson sample

For the Poisson a posterior distribution for the complete sample size, N, is derived from an incomplete sample when any specified subset of the classes are missing.Means as well as other posterior characteristics of N are obtained for two examples with various classes removed. For the special case of a truncated ‘missing zero class’ Poisson sample a simulation experiment is performed for the small ‘N=25’ sample situation applying both Bayesian and maximum likelihood methods of estimation.

Statistical inference for Markov processes when the model is incorrect

Statistical inference for Markov processes is commonly based on the maximum likelihood method of estimation and the likelihood ratio criterion for testing hypotheses. Construction of estimators and test statistics by these methods require that a model be chosen in the form of a family of transition density functions. In this paper, asymptotic properties of the maximum likelihood estimator and of the likelihood ratio statistic λn are examined when the model chosen for their construction is incorrect—that is, when no density in the model is a density for the transition probability distribution of the Markov process. It is shown that if and λn are constructed from a ‘regular’ incorrect model, then is consistent and asymptotically normally distributed and the asymptotic null distribution of −2 log λn is that of a linear combination of independent chi-squared random variables. These results are applied to propose measures of the performance of the test based on λn when the statistic is constructed from an incorrect model.

Statistical inference for Markov processes when the model is incorrect

Statistical inference for Markov processes is commonly based on the maximum likelihood method of estimation and the likelihood ratio criterion for testing hypotheses. Construction of estimators and test statistics by these methods require that a model be chosen in the form of a family of transition density functions. In this paper, asymptotic properties of the maximum likelihood estimator and of the likelihood ratio statistic λ n are examined when the model chosen for their construction is incorrect—that is, when no density in the model is a density for the transition probability distribution of the Markov process. It is shown that if and λ n are constructed from a ‘regular’ incorrect model, then is consistent and asymptotically normally distributed and the asymptotic null distribution of −2 log λ n is that of a linear combination of independent chi-squared random variables. These results are applied to propose measures of the performance of the test based on λ n when the statistic is constructed from an incorrect model.

Modified equation error method for aircraft parameter estimation

The problem of estimation of aircraft parameters is of considerable significance in the field of flight data reduction. Modified equation error method (MEEM) has been developed for the extraction of stability and control derivatives from given input and output ‘ flight ’ test data. The estimates as given by MEEM compare extremely well with a very sophisticated technique like the method of maximum likelihood estimation. It is found that the algorithm MEEM is simple and takes less time compared to the involved methods like the output error method. Further it is sufficient to measure only the derivatives of the states (linear and/or angular accelerations).

Estimation in Modified and Compound Modified Discrete Distributions

Three modified and three compound modified discrete probability distributions are presented along with certain assumptions which relate the models to appropriate physical situations. The modiJication is originally due to Singh (1963a). Modified minimum chi-square and maxin1um likelihood methods of estimation are discussed. Three types of physical situations involving births, thunderstorm activity and accidents are analyzed, applying the models and methods of estimation to appropriate sets of frequency data.

A Comparison of Methods for Analyzing Censored Life Data to Estimate Relationships Between Stress and Product Life

This article briefly reviews graphical, maximum likelihood, and linear estimation methods for analyzing censored life data to estimate relationships between stress and product life. Each method is illustrated by an example dealing with accelerated life test data on motor insulation. The advantages and disadvantages of the methods are compared to guide the choice of a method for a given application.

XX.—Some New Results in Maximum Likelihood Factor Analysis

SynopsisUntil now the chief obstacle to the application of the maximum likelihood method of estimation to factor analysis has been the lack of any really good numerical method of solution. In this paper we give a brief review of recent work which remedies this defect. Two factor analysis models are considered. In each case we derive results which are of use in connection with new methods of solution. Formulae are given for the large-sample variances and covariances of the estimates of parameters in the first model.

Efficient recursive estimation of the parameters of a radar or radio astronomy target

In radar or radio astronomy we observe a signal whose covariance function depends on some target parameters of interest. We consider here the problem of estimating the values of these parameters from our observation of the signal. One possible procedure is to use the method of maximum likelihood estimation. This method has the advantage that, as the duration of the observation interval becomes long, the mean square error in the maximum likelihood estimate approaches the minimum given by the Cramer-Rao bound. However, the maximum likelihood estimate is usually difficult to compute. We present here a recursive estimation procedure which divides the observation interval up into subintervals of short length; on each subinterval the signal is processed quadratically and the resulting calculation used to improve our estimate. This method has many computational advantages and, under certain conditions, we can show that the error in the resulting sequence of estimates approaches the Cramer-Rao bound. We begin by giving brief consideration to the problem of determining the functional dependence of the covariance function of the received signal on the target parameters. We then present expressions for the terms that appear in the Cramer-Rao inequality. Lastly, we describe the recursive estimation method and state conditions under which it is applicable.