Likelihood Estimation Method Research Articles

LSVL: Large-scale season-invariant visual localization for UAVs

Localization of autonomous unmanned aerial vehicles (UAVs) relies heavily on Global Navigation Satellite Systems (GNSS), which are susceptible to interference. Especially in security applications, robust localization algorithms independent of GNSS are needed to provide dependable operations of autonomous UAVs also in interfered conditions. Typical non-GNSS visual localization approaches rely on known starting pose, work only on a small-sized map, or require known flight paths before a mission starts. We consider the problem of localization with no information on initial pose or planned flight path. We propose a solution for global visual localization on large maps, based on matching orthoprojected UAV images to satellite imagery using learned season-invariant descriptors, and test with environment sizes up to 100 km2. We show that the method is able to determine heading, latitude and longitude of the UAV at 12.6–18.7 m lateral translation error in as few as 23.2–44.4 updates from an uninformed initialization, also in situations of significant seasonal appearance difference (winter–summer) between the UAV image and the map. We evaluate the characteristics of multiple neural network architectures for generating the descriptors, and likelihood estimation methods that are able to provide fast convergence and low localization error. We also evaluate the operation of the algorithm using real UAV data and evaluate running time on a real-time embedded platform. We believe this is the first work that is able to recover the pose of an UAV at this scale and rate of convergence, while allowing significant seasonal difference between camera observations and map.

Maximum $$\log _q$$ likelihood estimation for parameters of Weibull distribution and properties: Monte Carlo simulation

The maximum $${\log }_q$$ likelihood estimation method is a generalization of the known maximum $$\log $$ likelihood method to overcome the problem for modeling non-identical observations (inliers and outliers). The parameter q is a tuning constant to manage the modeling capability. Weibull is a flexible and popular distribution for problems in engineering. In this study, this method is used to estimate the parameters of Weibull distribution when non-identical observations exist. Since the main idea is based on modeling capability of objective function $$\rho (x;\varvec{\theta })=\log _q\big [f(x;\varvec{\theta })\big ]$$ , we observe that the finiteness of score functions cannot play a role in the robust estimation for inliers. The properties of Weibull distribution are examined. In the numerical experiment, the parameters of Weibull distribution are estimated by $$\log _q$$ and its special form, $$\log $$ , likelihood methods if the different designs of contamination into underlying Weibull distribution are applied. The optimization is performed via genetic algorithm. The modeling competence of $$\rho (x;\varvec{\theta })$$ and insensitiveness to non-identical observations are observed by Monte Carlo simulation. The value of q can be chosen by use of the mean squared error in simulation and the p value of Kolmogorov–Smirnov test statistic used for evaluation of fitting competence. Thus, we can overcome the problem about determining of the value of q for real data sets.

Farm Specific Technical Efficiency and Potential Output of Banana Crops in South Gujarat

The banana is an important fruit crop grown in Gujarat, especially in South Gujarat. The study aimed to estimate the technical efficiency of banana in South Gujarat by the maximum likelihood estimation (MLE) method using the stochastic frontier production function. The results revealed that the mean level of technical efficiency was 90, 93 and 90 per cent for small, medium and overall farmers, respectively. It indicated that on average, only 10, 6.67 and 8.33 per cent of the small, medium, and overall banana farmers fell short of the maximum possible frontier production technology, respectively. It also indicated the scope of improvement in the yield by managing significant and positive inputs by the respective categories of banana farmers. The potential output for small and medium farmers was 644 and 680.31 q per ha, which was 46 and 47.62 q per ha, more than the actual output. This loss in production was due to the inefficiency of managing input and other factors responsible for technical inefficiency. The factors affecting technical efficiencies suggested that the age of the farmers, household size, education and extension visit had a significant effect on the technical inefficiencies of the farmers.

Manly transformation in quantile regression: A comparison of two transformation parameter estimators

This study implements the Manly transformations for normalization of variables in quantile regression analysis.The transformation parameter was estimated using two different methods namely; the maximum likelihood estimation (MLE) method and the two-step estimation method by Chamberlain and Buchinsky(CBTS).The transformation parameters obtained using the two different methods were used for the Manly transformation of data with outliers and data without outliers. The methods were applied to a quantile regression analysis at different quantiles (0.25, 0.50, 0.75, 0.95). Based on our findings, for data without outliers, the 25th quantile model was seen to be the best fit model compared to the other quantiles for the CBTS method with AIC=-43.46279, BIC=20.75212 and MSE=0.70956, while for the MLE the 50th quantile model was seen to be the best fit model with AIC=-348.3657, BIC=20.13548, and MSE=0.00864. Considering data with outliers the 25th quantile model was still seen to be the best fit model compared to the other quantiles for the CBTS method with AIC=-48.5671, BIC=21.8321 and MSE=0.92341, while for the MLE the 50th quantile model was still seen to be the best fit model with AIC=988.6763, BIC=710.09, and MSE=690.7965. Comparison of both methods for data without outliers the study concludes that the estimation of the transformation parameter using the MLE produced better results with lower AIC, BIC and MSE at all quantiles and for data with outliers the study concludes that the estimation of the transformation parameter using CBTS produced better results with lower AIC, BIC and MSE results as is shown in table (3.5) and table (3.6) respectively.

Asymmetric Power Hazard Distribution for COVID-19 Mortality Rate under Adaptive Type-II Progressive Censoring: Theory and Inferences.

This article investigates the estimation of the parameters for power hazard function distribution and some lifetime indices such as reliability function, hazard rate function, and coefficient of variation based on adaptive Type-II progressive censoring. From the perspective of frequentism, we derive the point estimations through the method of maximum likelihood estimation. Besides, delta method is implemented to construct the variances of the reliability characteristics. Markov chain Monte Carlo techniques are proposed to construct the Bayes estimates. To this end, the results of the Bayes estimates are obtained under squared error and linear exponential loss functions. Also, the corresponding credible intervals are constructed. A simulation study is utilized to assay the performance of the proposed methods. Finally, a real data set of COVID-19 mortality rate is analyzed to validate the introduced inference methods.

Parametric inference of generalized process capability index Cpyk for the power Lindley distribution

ABSTRACT In this article, to estimate the generalized process capability index (GPCI) Cpyk when the process follows the power Lindley distribution, we have used five methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares method of estimation, the maximum product of spacings method of estimation, and Bayesian method of estimation. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential) loss functions with the help of the Metropolis-Hastings algorithm and importance sampling method. The confidence intervals for the GPCI Cpyk is constructed based on three bootstrap methods and Bayesian methods. Besides, asymptotic confidence intervals based on maximum likelihood method is also constructed. We studied the performances of these estimators based on their corresponding biases and MSEs for the point estimates of GPCI Cpyk, and coverage probabilities (CPs), and average width (AW) for interval estimates. It is found that the Bayes estimates performed better than the considered classical estimates in terms of their corresponding MSEs. Further, the Bayes estimates based on linear-exponential loss function are more efficient than the squared error loss function under informative prior. To illustrate the performance of the proposed methods, two real data sets are analyzed.In this article, to estimate the generalized process capability index (GPCI) when the process follows the power Lindley distribution, we have used five methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares method of estimation, the maximum product of spacings method of estimation, and Bayesian method of estimation. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential) loss functions with the help of the Metropolis-Hastings algorithm and importance sampling method. The confidence intervals for the GPCI is constructed based on three bootstrap methods and Bayesian methods. Besides, asymptotic confidence intervals based on maximum likelihood method is also constructed. We studied the performances of these estimators based on their corresponding biases and MSEs for the point estimates of GPCI , and coverage probabilities (CPs), and average width (AW) Abbreviations: AW : Average width; : Bias-corrected percentile bootstrap; BCI : Bootstrap confidence interval; CDF : Cumulative distribution function; CI : Confidence interval; CK : Coefficient of kurtosis; CP : Coverage probability; CS : Coefficient of skewness; GGD : Generalized gamma distribution; GPCI : Generalized process capability index; GLD : Generalized lindley distribution; SWCI : Shortest width credible interval; IS : Importance sampling; K-S : Kolmogorov-Smirnov; : Lower specification limi; LD : Lindley distribution; LDL : Lower desired limitLLF : Linex loss function; MCMC : Markov Chain Monte Carlo; MH : Metropolis-Hastings; MPSE : Maximum product of spacings estimator; MLE : Maximum likelihood estimator; MSE : Mean squared error; OLSE : Ordinary least squares estimator; : Percentile bootstrap; PDF : Probability density function; PCI : Process capability index; PLD : Power Lindley distribution; : -th quartile; SD : Standard deviation; : Standard bootstrap; SELF : Squared error loss function; : Target value; : Upper specification limit; : Upper desired limit; WD : Weibull distribution; WLSE : Weighted least squares estimator

Technical Efficiency of Lobster (Panulirus sp) Farming in East Lombok Regency

East Lombok Regency is one of the centers for the development of aquaculture and the largest lobster seed producer in Indonesia. However, in terms of productivity, lobster cultivation is still relatively low due to the less optimal use of production factors and management in carrying out lobster rearing cultivation. The purpose of this study was to analyze the factors that affect the production of lobster rearing aquaculture and to analyze the level of technical efficiency and the factors that influence the technical inefficiency of lobster rearing aquaculture in East Lombok Regency. Descriptive research method was selected in this research. Cross section data was collected using a survey technique on 40 respondents who were selected by simple random sampling. The collected data was then analyzed using the Cobb-Douglas Stochastic Frontier production function with the Maximum Likelihood Estimator (MLE) method. The results showed that the production of lobster rearing aquaculture in East Lombok Regency was significantly influenced at the alpha level 5% by the variables of the number of cages, feed, number of family dependents and dummy species. The level of technical efficiency of lobster rearing cultivation is classified as efficient with a technical efficiency value of 0.94. Then the factors that affect the inefficiency of lobster rearing business in East Lombok Regency include age, education level and training dummy.

China trade with belt and road countries: the role and impact of institutions

ABSTRACT This article investigates the impact of institutional quality on China’s trade with belt and road economies by testing the augmented gravity model framework. Our empirical analysis is based on 16 years of balanced panel data of 65 belt and road economies. We use the instrumental variable estimator developed for a panel data model to address the potential endogeneity issue. We distinguish the vital role of institutions in trading partner countries in shaping this result. Our outcomes outline an interesting story about the association between institutional quality and China’s export to and import from belt and road countries. We find that the weaker voice and accountability and political stability in B&R countries negatively affect China exports, while China import from B&R economies shows a statistically positive effect of institutions. Our findings are robust to employs a panel pseudo-maximum likelihood (PPML) estimation method. As part of wider trade integration, we conclude that the B&R countries should strengthen their institutions. The results of this study have several implications for policymakers.

Marshall-Olkin Alpha Power Rayleigh Distribution: Properties, Characterizations, Estimation and Engineering applications

In this paper, we introduce a new there-parameter Rayleigh distribution, called the Marshall-Olkin alpha power Rayleigh (MOAPR) distribution. Some statistical properties of the MOAPR distribution are obtained. The proposed model is characterized based on truncated moments and reverse hazard function. The maximum likelihood and bootstrap estimation methods are considered to estimate the MOPAR parameters. A Monte Carlo simulation study is performed to compare the maximum likelihood and bootstrap estimation methods. Superiority of the MOAPR distribution over some well-known distributions is illustrated by means of two real data sets.

Real Estate Credit and Liquidity Risk with Ownership Structure as Moderating Variables in Banking Companies Listed on The Indonesia Stock Exchange

The purpose of this study is to investigate the effect of real estate credit on liquidity risk. This study also looked at the role of government ownership and foreign ownership in moderating the effect of real estate credit on bank liquidity risk. There are 43 banking companies listed on the Indonesia Stock Exchange for the 2014-2018 period used as samples. This study used a multiple linear regression model with the Ordinary Least Square (OLS) estimation method and robustness tests using the Maximum Likelihood (MLE) estimation method. The results of this study concluded that real estate credit has a significant positive effect on liquidity risk. Government ownership strengthens the positive effect of real estate credit on liquidity risk, while foreign ownership weakens the positive effect of real estate credit on liquidity risk.

Inverse Gaussian Liu-type estimator

The inverse Gaussian regression (IGR) model parameters are generally estimated using the maximum likelihood (ML) estimation method. Since the multicollinearity problem exists among the explanatory variables, the ML estimation method becomes inflated. When the multicollinearity problem occurs, biased estimators can be used to estimate the parameters of the model. One of the most widely used biased estimators is the Liu-type estimator. In this study, we extend the Liu-type estimator for the IGR model. The proposed estimator is compared with the Ridge and Liu estimators defined for the IGR model in terms of the mean squared error (MSE) criterion. Also, a real data example is presented to illustrate the superiority of the proposed estimator. Experimental results show that the Liu-type estimator outperforms the Ridge and Liu estimators when multicollinearity exists.

A Novel Method for Developing Efficient Probability Distributions with Applications to Engineering and Life Science Data

In this paper, a new approach for deriving continuous probability distributions is developed by incorporating an extra parameter to the existing distributions. Frechet distribution is used as a submodel for an illustration to have a new continuous probability model, termed as modified Frechet (MF) distribution. Several important statistical properties such as moments, order statistics, quantile function, stress-strength parameter, mean residual life function, and mode have been derived for the proposed distribution. In order to estimate the parameters of MF distribution, the maximum likelihood estimation (MLE) method is used. To evaluate the performance of the proposed model, two real datasets are considered. Simulation studies have been carried out to investigate the performance of the parameters’ estimates. The results based on the real datasets and simulation studies provide evidence of better performance of the suggested distribution.

APPLICATIONS OF INVERSE WEIBULL RAYLEIGH DISTRIBUTION TO FAILURE RATES AND VINYL CHLORIDE DATA SETS

In this work, a new three parameter distribution called the Inverse Weibull Rayleigh distribution is proposed. Some of its statistical properties were presented. The PDF plot of Inverse Weibull Rayleigh distribution showed that it is good for modeling positively skewed and symmetrical datasets. The plot of the hazard function showed that the proposed distribution can fit datasets with bathtub shape. Method of maximum likelihood estimation was employed to estimate the parameters of the distribution, the estimators of the parameters of Inverse Weibull Rayleigh distribution is asymptotically unbiased and asymptotically efficient from the result of the simulation carried out. Applying the new distribution to a positively skewed Vinyl Chloride data set shows that the distribution performs better than Rayleigh, Generalized Rayleigh, Weibull Rayleigh, Inverse Weibull, Inverse Weibull Weibull, Inverse Weibull Inverse Exponential and Inverse Weibull Pareto distribution in fitting the data as it has the smallest AIC value. Also, applying the new distribution to a negatively skewed bathtub shape failure rates data shows that the distribution is a competitive model after Weibull Rayleigh and Inverse Weibull Weibull distributions in fitting the data because it has the third least AIC value.

A new one parameter discrete distribution and its applications

In this paper, a new one parameter discrete distribution which is better than several well-known one parameter discrete distributions has been proposed. The expressions for its coefficient of variation, skewness, kurtosis and index of dispersion have been obtained and their behaviors illustrated graphically. The method of moment and the method of maximum likelihood estimation for estimating the parameter have been discussed. The simulation study has also been presented in order to illustrate the performance of maximum likelihood estimator. The goodness of fit of the proposed distribution has been explained with three examples of count datasets and its fit was found quite satisfactory over Poisson distribution, Poisson-Lindley distribution, Poisson-Akash distribution and Poisson-Ishita distribution.

A New Extended Geometric Distribution: Properties, Regression Model, and Actuarial Applications

In this paper, a new modified version of geometric distribution is proposed. The newly introduced model is called transmuted record type geometric (TRTG) distribution. TRTG distribution is a good alternative to the negative binomial, Poisson and geometric distributions in modeling real data encountered in several applied fields. The main statistical properties of the new distribution were obtained. We determined the measures of value at risk and tail value at risk for the TRTG distribution. These measures are important quantities in actuarial sciences for portfolio optimization under uncertainty. The TRTG parameters were estimated via maximum likelihood, moments, proportions, and Bayesian estimation methods, and the simulation results were determined to explore their performance. Furthermore, a new count regression model based on the TRTG distribution was proposed. Four real data applications were adopted to illustrate the applicability of the TRTG distribution and its count regression model. These applications showed empirically that the TRTG distribution outperforms some important discrete models such as the negative binomial, transmuted geometric, discrete Burr, discrete Chen, geometric, and Poisson distributions.

A new flexible logarithmic transform heavy-tailed distribution and its applications

This paper aims to propose a new right skewed, heavy tailed probability distribution with upside-down bathtub shape hazard rate. The related statistical characteristics and its measures are derived. The unknown parameter of the proposed distribution is estimated by using five estimation methods, namely maximum likelihood estimation (MLE) method, maximum product spacing estimation (MPSE) method, least square estimation (LSE) method, weighted least square estimation method and Cramer-Von-Mises estimation (CVME) method. Also, asymptotic confidence interval (ACI) and bootstrap confidence intervals (BCIs) namely, standard bootstrap (s-boot), percentile bootstrap (p-boot), and Student’s bootstrap (t-boot) of the parameter are also computed. The Monte Carlo simulation study has been performed to compare the performance of the proposed estimators and corresponding interval width along with coverage probability. At last, three real data sets have been used to demonstrate the suitability of the proposed study in real life scenario. The considered data sets also exhibit skewed, heavy tailed, upside-down bathtub shape hazard rate pattern.

Enhancement of light aircraft 6 DOF simulation using flight test data in longitudinal motion

Abstract This paper proposes a procedure to improve the accuracy of the light aircraft 6 DOF simulation model by implementing model tuning and aerodynamic database correction using flight test data. In this study, the full-scale flight testing of a 2-seater aircraft has been performed in specific longitudinal manoeuver for model enhancement and simulation validation purposes. The baseline simulation model database is constructed using multi-fidelity analysis methods such as wind tunnel (W/T) test, computational fluid dynamic (CFD) and empirical calculation. The enhancement process starts with identifying longitudinal equations of motion for sensitivity analysis, where the effect of crucial parameters is analysed and then adjusted using the model tuning technique. Next, the classical Maximum Likelihood (ML) estimation method is applied to calculate aerodynamic derivatives from flight test data, these parameters are utilised to correct the initial aerodynamic table. A simulation validation process is introduced to evaluate the accuracy of the enhanced 6 DOF simulation model. The presented results demonstrate that the applied enhancement procedure has improved the simulation accuracy in longitudinal motion. The discrepancy between the simulation and flight test response showed significant improvement, which satisfies the regulation tolerance.

Wrapped modified Lindley distribution

To model data in angular form, circular distributions are the most appropriate mathematical tools. In this paper, we introduce a new one-parameter circular distribution based on the wrapping method, called the wrapped modified Lindley distribution. Characteristic function and fundamental properties of this distribution are described. Method of maximum likelihood estimation is used for the estimation of the parameter. The proposed model is applied to two real-life datasets, and its performance is compared with that of the wrapped Lindley, wrapped exponential and transmuted wrapped exponential models.

Reliability estimation of the stress–strength model with non-identical jointly type-II censored Weibull component strengths

ABSTRACT This article considers the estimation of the stress–strength reliability with non-identical and also jointly censored component strengths. Both stress and strength variables are assumed to follow two-parameter Weibull distribution. In this reliability model, we assume type-II censoring scheme for common stress variable and jointly type-II censoring scheme for strength variables. Inferences for the reliability of this system are obtained with maximum likelihood estimation (MLE) and Bayesian estimation methods. In the Bayesian section, point estimations are obtained with Lindley's approximation and Markov Chain Monte Carlo method with the Metropolis-Hasting algorithm. Also, asymptotic confidence intervals for the MLEs and the highest posterior density credible intervals for Bayesian estimations are obtained. Theoretical outcomes are illustrated with simulation studies and a real data example.

Ranked set sampling with application of modified Kies exponential distribution

This paper is concerned with estimating the parameters of the modified Kies exponential (MKEx) distribution using the classical estimation method, based on ranked set sampling (RSS), Likelihood estimation method is used for estimating the MKEx parameters. The maximum likelihood estimators (MLEs) are then investigated and compared to the corresponding ones based on simple random sampling (SRS) and RSS designs. A Monte Carlo simulation is used to obtain the absolute relative biases, mean square errors for the MKEx distribution. Efficiencies are compared for the different designs. The relative efficiency of RSS design was found to increase with increasing the number of cycles, compared with other designs for the MKEx distribution.