Parameter Estimation for Composite Dynamical Systems Based on Sequential Order Statistics from Burr Type XII Mixture Distribution

It is known that various types of location privacy attacks can be carried out using a personalized transition matrix that is learned for each target user, or a population transition matrix that is common to all target users. However, since many users disclose only a small amount of location information in their daily lives, the training data can be extremely sparse. The aim of this paper is to clarify the risk of location privacy attacks in this realistic situation. To achieve this aim, we propose a learning method that uses tensor factorization (or matrix factorization) to accurately estimate personalized transition matrices (or a population transition matrix) from a small amount of training data. To avoid the difficulty in directly factorizing the personalized transition matrices (or population transition matrix), our learning method first factorizes a transition count tensor (or matrix), whose elements are the number of transition counts that the user has made, and then normalizes counts to probabilities. We focus on a localization attack, which derives an actual location of a user at a given time instant from an obfuscated trace, and compare our learning method with the maximum likelihood (ML) estimation method in both the personalized matrix mode and the population matrix mode. The experimental results using four real data sets show that the ML estimation method performs only as well as a random guess in many cases, while our learning method significantly outperforms the ML estimation method in all of the four data sets.

When analyzing censored datasets, where one or more measurements are below the limit of detection (LOD), the maximum likelihood estimation (MLE) method is often considered the gold standard for estimating the GM and GSD of the underlying exposure profile. A new and relatively simple substitution method, called β -substitution, is presented and compared with the MLE method and the common substitution methods (LOD/2 and LOD/√2 substitution) when analyzing a left-censored dataset with either single or multiple censoring points. A computer program was used to generate censored exposure datasets for various combinations of true geometric standard deviation (1.2 to 4), percent censoring (1% to 50%), and sample size (5 to 19 and 20 to 100). Each method was used to estimate four parameters of the lognormal distribution: (1) the geometric mean, GM; (2) geometric standard deviation, GSD; (3) 95th percentile, and (4) Mean for the censored datasets. When estimating the GM and GSD, the bias and root mean square error (rMSE) for the β -substitution method closely matched those for the MLE method, differing by only a small amount, which decreased with increasing sample size. When estimating the Mean and 95th percentile the β -substitution method bias results closely matched or bettered those for the MLE method. In addition, the overall imprecision, as indicated by the rMSE, was similar to that of the MLE method when estimating the GM, GSD, 95th percentile, and Mean. The bias for the common substitution methods was highly variable, depending strongly on the range of GSD values. The β-substitution method produced results comparable to the MLE method and is considerably easier to calculate, making it an attractive alternative. In terms of bias it is clearly superior to the commonly used LOD/2 and LOD/√2 substitution methods. The rMSE results for the two substitution methods were often comparable to rMSE results for the MLE method, but the substitution methods were often considerably biased.

Travel Time Reliability Estimation Model Using Observed Link Flows in a Road Network

Estimating the failure rate of the log-logistic distribution by smooth adaptive and bias-correction methods

In this paper, we study the modified Weibull extension distribution by utilizing the Monte Carlo method in the simulation procedure to generate various sample sizes with various replicates of the sample size and using this simulation to compare two estimation methods, the maximum likelihood estimator method and the rank set sampling estimator method, to get the best estimate for the unknown parameters of the modified Weibull extension distribution. It is noted that mean square error values for the maximum likelihood estimator method are better than mean square error values for the rank set sampling estimator method, which means that the maximum likelihood estimator method is the best for estimating the parameters of the modified Weibull extension distribution. Accordingly, we obtain an initial value from the best estimation for starting the process of applying this study in our lives on real data about patients who suffer from acute lymphocytic leukemia disease, and estimate the Survival and hazard functions of this state of patients.

The Lognormal distribution has been widely used to represent the type of air pollutant concentration distribution. There are different methods to estimate the distribution parameters such as the method of moments, percentiles, maximum likelihood estimation (MLE) and Bayesian method of estimation. In this study, the theoretical distribution Lognormal is used to fit the parent distribution of PM 10 of Putalisadak of Kathmandu, Nepal. Two estimating methods namely method of maximum likelihood and method of moments are used to estimate the parameters of the theoretic distributions.

In weak GNSS signal environments, extending integration time is paramount to improving the GNSS receiver's sensitivity. Furthermore, sufficient coherent integration can help to separate the line-of-sight (LOS) and non LOS (NLOS) signals — primarily in the Doppler domain — for multipath mitigation. However, extending integration time is limited by the presence of the navigation message data bits. The Maximum-Likelihood (ML) estimation method has been shown as the most effective way to estimate the navigation bit boundary locations (i.e., bit synchronization) and subsequently estimate the data bit values (i.e., bit decoding) in the presence of noise alone. This paper further analyzes the performance of ML estimation method as a function of various other parameters by using the successful synchronization rate (SSR) and successful decoding rate (SDR) as the criteria. The parameters considered include the number of data bits required (i.e., integration time) and the Doppler frequency error, and both are evaluated under different signal strength scenarios. The requirements for bit synchronization are analyzed under three SSRs, which are 85%, 90% and 95%. Results indicate that, under the SSR of 90% and the SDR of 90%, bit synchronization and bit decoding are valid for signal strengths of 15 dB-Hz and 20 dB-Hz respectively, and the Doppler frequency errors should not be larger than 24 Hz and 11 Hz respectively.

The Gompertz-Lindley distribution is an extension of the Lindley distribution with three parameters. It was found to be more flexible for modeling real life events. The distribution contains two shape parameters and a scale parameter. Despite the necessity of parameter estimation theory in modeling, it has not been shown that a method of estimation method is better for any of these three parameters of the Gompertz-Lindley distribution. This paper identifies the best estimation method for the shape parameter of the Gompertz-Lindley distribution by deriving Bayesian estimators for the shape parameter of the distribution using two non-informative prior distributions (Uniform and Jeffery) and an informative prior (gamma) under squared error loss function (SELF), quadratic loss function (QLF) and precautionary loss function (PLF). These estimators were evaluated and the results compared with the maximum likelihood estimation method using Monte Carlo simulations with the mean square error (MSE) as a criterion for choosing the best estimator.

Population density is an important state variable in ecology and monitoring of wildlife populations. In the study of large carnivores, traditional density estimation methods have relied on camera trapping to collect capture–recapture data using sampling designs suited to a single target species and ad hoc methods to calculate the effective trapping area. We describe an application of spatially explicit capture–recapture analysis to estimate density for four sympatric carnivore species using a standard spatial sampling grid, camera trap sampling, and maximum-likelihood estimation methods. We used camera traps deployed in four adjacent, sequential camera arrays to construct capture histories for leopard, aardwolf, spotted hyena, and striped hyena in an African savanna/scrub ecosystem. We considered two methods of constructing trapping histories: (1) a simultaneous layout in which all cameras are deployed and active for 21 trapping intervals of 24 h each; and (2) an incomplete layout in which cameras are considered deployed for 84 sampling intervals, but with only a fraction of traps active for a given sampling interval. We estimated density and confidence or profile likelihood intervals for each species using a mean maximum distance moved method and maximum-likelihood estimation procedures with model averaging. Maximum-likelihood densities ranged from 4.93/100 km2 for spotted hyena to 12.03/100 km2 for leopard. Estimates did not differ between simultaneous and incomplete trap layouts. Our approach demonstrates the utility and cost effectiveness of using maximum-likelihood density estimation methods in studies of sympatric species that are individually recognizable.

Two-parameter Weibull distribution is the most widely adopted lifetime model for power transformers. An appropriate parameter estimation method is essential to guarantee the accuracy of a derived Weibull lifetime model. Six popular parameter estimation methods (i.e. the maximum likelihood estimation method, two median rank regression methods including the one regressing X on Y and the other one regressing Y on X, the Kaplan-Meier method, the method based on cumulative hazard plot, and the Li's method) are reviewed and compared in order to find the optimal one that suits transformer's Weibull lifetime modelling. The comparison took several different scenarios into consideration: 10000 sets of lifetime data, each of which had a sampling size of 40 1000 and a censoring rate of 90\%, were obtained by Monte-Carlo simulations for each scienario. Scale and shape parameters of Weibull distribution estimated by the six methods, as well as their mean value, median value and 90\% confidence band are obtained. The cross comparison of these results reveals that, among the six methods, the maximum likelihood method is the best one, since it could provide the most accurate Weibull parameters, i.e. parameters having the smallest bias in both mean and median values, as well as the shortest length of the 90\% confidence band. The maximum likelihood method is therefore recommended to be used over the other methods in transformer Weibull lifetime modelling.

In this paper, it was obtained estimators of the scale parameter of Extended Poisson Exponential distribution by four methods using complete data, these methods are the Maximum Likelihood Estimator (MLE), the Least Squares Estimator (LSE), Plotting Position Estimator (PPE) and White Estimator (WE), these four methods have been compared by the criteria of Mean Square Error (MSE) using Monte Carlo simulation, and from the results on the samples in the simulation, the comparison in this study showed that Maximum Likelihood Estimator method is best from other methods followed by the White Estimator method then the Least Squares Estimator method.

This study aims to compare the efficacy of logistic regression model for identifying the risk factors of low-birth-weight babies in Indonesia using the maximum likelihood estimation (MLE)and the Bayesian estimation methods. The data used in this study is secondary data derived from the 2017 Indonesian Demographic Health Survey with a total sample of 16,344 newborn babies. Selection of the best logistic regression model was based on the smaller Bayesian Schwartz Information Criterion (BIC) value. The logistic regression model with the Bayesian estimation method has a smaller BIC value than the MLE method. Twin births, baby girl, maternal age at risk, birth spacing that is too close, iron deficiency, low education, low economy, inadequate drinking water sources have provided a higher risk of low-birth-weight incidence.

Recent catastrophic failures of the rocket motor on a US missile caused concern in the US Navy that the missile might not be serviceable past its estimated service life of 20 years. This paper analyzes nearly 2000 firings of the motor under field conditions using classical maximum likelihood estimation (MLE) methods and Bayesian methods. MLE methods indicate that there could be less than a 1% chance that the motor will survive past 20 years of life and are not considered credible. Bayesian methods indicate that there is better than a 99% chance that the motors will survive past 20 years of life. The authors present reasons for preferring the Bayesian analysis and discuss testing schemes for more precise estimates. They comment on the lack of data to perform degradation analysis as a function of temperature cycling for the motor and make recommendations for future missile system data collection.

Univariate Weibull distribution is a well known lifetime distribution and has been widely used in reliability and survival analysis. In this paper, we introduce a new family of bivariate generalized Weibull (BGW) distributions, whose univariate marginals are exponentiated Weibull distribution. Different statistical quantiles like marginals, conditional distribution, conditional expectation, product moments, correlation and a measure component reliability are derived. Various measures of dependence and statistical properties along with aging properties are examined. Further, the copula associated with BGW distribution and its various important properties are also considered. The methods of maximum likelihood and Bayesian estimation are employed to estimate unknown parameters of the model. A Monte Carlo simulation and real data study are carried out to demonstrate the performance of the estimators and results have proven the effectiveness of the distribution in real-life situations.

Weibull distribution is widely used in various areas such as life tables, failure rates, and definition of wind speed distribution. Therefore, parameter estimation for the Weibull distribution is an important problem in many real data applications. The least square (LS), the weighted least square (WLS) and the maximum likelihood (ML) are the most popular methods for the parameter estimation in the Weibull distribution. In this study, based on the LS, WLS and ML estimation methods, a multi-objective programming approach is proposed for the parameter estimation of two-parameter Weibull distribution. This new approach evaluates together LS, WLS and ML methods in the estimation process. NSGA-II method, which is a multi-objective heuristic optimization method, is used to solve the proposed multi-objective estimation model. To evaluate the applicability and performance of the proposed approach, a detailed Monte Carlo simulation study based on deficiency criteria and a real data application are designed. The results illustrated that the proposed multi-objective programming approach provides quite accurate parameter estimates for the two parameter Weibull distribution with respect to deficiency criteria.