scholarly journals A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 835 ◽  
Author(s):  
Lorentz Jäntschi
Keyword(s):  
Continuous Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Sampling Distribution ◽  
Cumulative Distribution ◽  
Experimental Science ◽  
Continuous Distributions ◽  
Statistical Parameters ◽  
Rich Information ◽  
Maximum Likelihood Estimation Method

One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling distribution) provides rich information for any estimation to be made. Distributions are split into two main groups: continuous and discrete. The present study applies to continuous distributions. One of the challenges of sampling is its accuracy, or, in other words, how representative the sample is of the population from which it was drawn. To answer this question, a series of statistics have been developed to measure the agreement between the theoretical (the population) and observed (the sample) distributions. Another challenge, connected to this, is the presence of outliers - regarded here as observations wrongly collected, that is, not belonging to the population subjected to study. To detect outliers, a series of tests have been proposed, but mainly for normal (Gauss) distributions—the most frequently encountered distribution. The present study proposes a statistic (and a test) intended to be used for any continuous distribution to detect outliers by constructing the confidence interval for the extreme value in the sample, at a certain (preselected) risk of being in error, and depending on the sample size. The proposed statistic is operational for known distributions (with a known probability density function) and is also dependent on the statistical parameters of the population—here it is discussed in connection with estimating those parameters by the maximum likelihood estimation method operating on a uniform U(0,1) continuous symmetrical distribution.

scholarly journals The Maxwell – Exponential Distribution: Theory and Application to Lifetime Data

2021 ◽  
Vol 3 (2) ◽  
pp. 65-80
Author(s):  
Usman Aliyu Abdullahi ◽  
Ahmad Abubakar Suleiman ◽  
Aliyu Ismail Ishaq ◽  
Abubakar Usman ◽  
Aminu Suleiman
Keyword(s):  
Exponential Distribution ◽  
Survival Function ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Information Criteria ◽  
Cumulative Distribution ◽  
Two Parameters ◽  
Maximum Likelihood Estimation Method

Two parameters Maxwell – Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function, and statistical properties of the proposed distribution are discussed. The parameters of the proposed distribution have been estimated using the maximum likelihood estimation method. The potentiality of the estimators was shown using a simulation study. The overall assessment of the performance of Maxwell - Exponential distribution was determined by using two real-life datasets. Our findings reveal that the Maxwell – Exponential distribution is more flexible compared to other competing distributions as it has the least value of information criteria.

scholarly journals On Wrapping of Quasi Lindley Distribution

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 930
Author(s):  
Ahmad M. H. Al-khazaleh ◽  
Shawkat Alkhazaleh
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Estimation Of Parameters ◽  
Circular Distribution ◽  
Lindley Distribution ◽  
Trigonometric Moments ◽  
Maximum Likelihood Estimation Method

In this paper, as an extension of Wrapping Lindley Distribution (WLD), we suggest a new circular distribution called the Wrapping Quasi Lindley Distribution (WQLD). We obtain the probability density function and derive the formula of a cumulative distribution function, characteristic function, trigonometric moments, and some related parameters for this WQLD. The maximum likelihood estimation method is used for the estimation of parameters.

scholarly journals A multi-group higher-order factor analysis for studying the gender-effect in Teacher Job Satisfaction

METRON ◽  
2021 ◽  
Author(s):  
Carlo Cavicchia ◽  
Pasquale Sarnacchiaro
Keyword(s):  
Job Satisfaction ◽  
Factor Analysis ◽  
Secondary School Teachers ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Higher Order ◽  
Teacher Job Satisfaction ◽  
Public Secondary School ◽  
Order Factor ◽  
Maximum Likelihood Estimation Method

AbstractTeachers’ performances also depend on whether and how they are satisfied with their job. Therefore, Teacher Job Satisfaction must be considered as the driver of teachers’ accomplishments. To plan future policies and improve the overall teaching process, it is crucial to understand which factors mostly contribute to Teacher Job Satisfaction. A Common Assessment Framework and Education questionnaire was administered to 163 Italian public secondary school teachers to collect data, and a second-order factor analysis was used to detect which factors impact on Teacher Job Satisfaction, and to what extent. This model-based approach guarantees to detect factors which respect important properties: unidimensionality and reliability. All the coefficients are estimated according to the maximum likelihood estimation method in order to make inference on the parameters and on the validity of the model. Moreover, a new multi-group test for higher-order factor analysis was proposed and implemented. Finally, we analyzed in detail whether the factors impacting Teacher Job Satisfaction are characterized by gender.

scholarly journals A Bi-Level Weibull Model with Applications to Two Ordered Events

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Shuguang Song ◽  
Hanlin Liu ◽  
Mimi Zhang ◽  
Min Xie
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Mixture Distribution ◽  
Likelihood Estimation ◽  
Random Variable ◽  
Weibull Model ◽  
Reliability Function ◽  
The Other ◽  
Regularity Conditions ◽  
Maximum Likelihood Estimation Method

In this paper, we propose and study a new bivariate Weibull model, called Bi-levelWeibullModel, which arises when one failure occurs after the other. Under some specific regularity conditions, the reliability function of the second event can be above the reliability function of the first event, and is always above the reliability function of the transformed first event, which is a univariate Weibull random variable. This model is motivated by a common physical feature that arises fromseveral real applications. The two marginal distributions are a Weibull distribution and a generalized three-parameter Weibull mixture distribution. Some useful properties of the model are derived, and we also present the maximum likelihood estimation method. A real example is provided to illustrate the application of the model.

scholarly journals Detecting long-memory: Monte Carlo simulations and application to daily streamflow processes

2006 ◽  
Vol 3 (4) ◽  
pp. 1603-1627 ◽  
Author(s):  
W. Wang ◽  
P. H. A. J. M. van Gelder ◽  
J. K. Vrijling ◽  
X. Chen
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Long Memory ◽  
Positive Relationship ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Large Data ◽  
Daily Streamflow ◽  
Maximum Likelihood Estimation Method

Abstract. The Lo's R/S tests (Lo, 1991), GPH test (Geweke and Porter-Hudak, 1983) and the maximum likelihood estimation method implemented in S-Plus (S-MLE) are evaluated through intensive Mote Carlo simulations for detecting the existence of long-memory. It is shown that, it is difficult to find an appropriate lag q for Lo's test for different AR and ARFIMA processes, which makes the use of Lo's test very tricky. In general, the GPH test outperforms the Lo's test, but for cases where there is strong autocorrelations (e.g., AR(1) processes with φ=0.97 or even 0.99), the GPH test is totally useless, even for time series of large data size. Although S-MLE method does not provide a statistic test for the existence of long-memory, the estimates of d given by S-MLE seems to give a good indication of whether or not the long-memory is present. Data size has a significant impact on the power of all the three methods. Generally, the power of Lo's test and GPH test increases with the increase of data size, and the estimates of d with GPH test and S-MLE converge with the increase of data size. According to the results with the Lo's R/S test (Lo, 1991), GPH test (Geweke and Porter-Hudak, 1983) and the S-MLE method, all daily flow series exhibit long-memory. The intensity of long-memory in daily streamflow processes has only a very weak positive relationship with the scale of watershed.

scholarly journals A Stochastic Model of Stress Evolution in a Bolted Structure in the Presence of a Joint Elastic Piece: Modeling and Parameter Inference

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Mohammed Haiek ◽  
Youness El Ansari ◽  
Nabil Ben Said Amrani ◽  
Driss Sarsri
Keyword(s):  
Numerical Simulation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Model ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Stress Evolution ◽  
Parameter Inference ◽  
Maximum Likelihood Estimation Method ◽  
Over Time

In this paper, we propose a stochastic model to describe over time the evolution of stress in a bolted mechanical structure depending on different thicknesses of a joint elastic piece. First, the studied structure and the experiment numerical simulation are presented. Next, we validate statistically our proposed stochastic model, and we use the maximum likelihood estimation method based on Euler–Maruyama scheme to estimate the parameters of this model. Thereafter, we use the estimated model to compare the stresses, the peak times, and extinction times for different thicknesses of the elastic piece. Some numerical simulations are carried out to illustrate different results.

scholarly journals Calibration of MEMS Triaxial Accelerometers Based on the Maximum Likelihood Estimation Method

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yifan Sun ◽  
Xiang Xu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Random Noise ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Least Square ◽  
Triaxial Accelerometer ◽  
Zero Bias ◽  
Estimation Function ◽  
Maximum Likelihood Estimation Method

As a widely used inertial device, a MEMS triaxial accelerometer has zero-bias error, nonorthogonal error, and scale-factor error due to technical defects. Raw readings without calibration might seriously affect the accuracy of inertial navigation system. Therefore, it is necessary to conduct calibration processing before using a MEMS triaxial accelerometer. This paper presents a MEMS triaxial accelerometer calibration method based on the maximum likelihood estimation method. The error of the MEMS triaxial accelerometer comes into question, and the optimal estimation function is established. The calibration parameters are obtained by the Newton iteration method, which is more efficient and accurate. Compared with the least square method, which estimates the parameters of the suboptimal estimation function established under the condition of assuming that the mean of the random noise is zero, the parameters calibrated by the maximum likelihood estimation method are more accurate and stable. Moreover, the proposed method has low computation, which is more functional. Simulation and experimental results using the consumer low-cost MEMS triaxial accelerometer are presented to support the abovementioned superiorities of the maximum likelihood estimation method. The proposed method has the potential to be applied to other triaxial inertial sensors.

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