ESTIMATING THE SHAPE PARAMETER OF THE LOG-LOGISTIC DISTRIBUTION

2006 ◽  
Vol 13 (03) ◽  
pp. 257-266 ◽  
Author(s):  
ZHENMIN CHEN
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Confidence Intervals ◽  
Shape Parameter ◽  
Interval Estimation ◽  
Maximum Likelihood Estimators ◽  
Logistic Distribution ◽  
Pivotal Quantity ◽  
Estimation Problems ◽  
Exact Confidence Intervals

The log-logistic distribution is a useful distribution in survival analysis. Parameter estimation problems have been discussed by many authors. This paper focuses on the interval estimation for the shape parameter of the log-logistic distribution. Bain and Engelhardt3 gave confidence intervals for the parameters of a logistic distribution based on pivotal quantities formed by maximum likelihood estimators. Chen10 proposed another method for obtaining exact confidence intervals of the shape parameter of the log-logistic distribution. Compared with the existing methods for constructing confidence intervals for the parameters of the log-logistic distribution, the method given in Chen10 is easier to use. In the present paper, the pivotal quantity used in Chen10 is adjusted to improve the performance of statistical analysis. Monte Carlo simulation is conducted to compare the performance of different pivotal quantities. The simulation result shows that the adjusted pivotal quantity has better performance, and then should be recommended to the statistics users.

Monte Carlo simulation and analysis of free-form surface registration

1997 ◽  
Vol 211 (8) ◽  
pp. 605-617 ◽  
Author(s):  
D Brujic ◽  
M Ristic
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Confidence Intervals ◽  
Computer Aided Design ◽  
Maximum Error ◽  
Surface Registration ◽  
Performance Criteria ◽  
Free Form ◽  
Registration Method ◽  
Free Form Surfaces

Accurate dimensional inspection and error analysis of free-form surfaces requires accurate registration of the component in hand. Registration of surfaces defined as non-uniform rational B-splines (NURBS) has been realized through an implementation of the iterative closest point method (ICP). The paper presents performance analysis of the ICP registration method using Monte Carlo simulation. A large number of simulations were performed on an example of a precision engineering component, an aero-engine turbine blade, which was judged to possess a useful combination of geometric characteristics such that the results of the analysis had generic significance. Data sets were obtained through CAD (computer aided design)-based inspection. Confidence intervals for estimated transformation parameters, maximum error between a measured point and the nominal surface (which is extremely important for inspection) mean error and several other performance criteria are presented. The influence of shape, number of measured points, measurement noise and some less obvious, but not less important, factors affecting confidence intervals are identified through statistical analysis.

scholarly journals Parametric inference of Akash distribution for Type-Ⅱ censoring with analyzing of relief times of patients

2021 ◽  
Vol 6 (10) ◽  
pp. 10789-10801
Author(s):  
Tahani A. Abushal ◽  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Bayesian Inference ◽  
Unknown Parameter ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Posterior Density ◽  
Monte Carlo Simulation Study ◽  
Reliability Characteristics ◽  
Highest Posterior Density

<abstract><p>In this paper, the problem of estimating the parameter of Akash distribution applied when the lifetime of the product follow Type-Ⅱ censoring. The maximum likelihood estimators (MLE) are studied for estimating the unknown parameter and reliability characteristics. Approximate confidence interval for the parameter is derived under the s-normal approach to the asymptotic distribution of MLE. The Bayesian inference procedures have been developed under the usual error loss function through Lindley's technique and Metropolis-Hastings algorithm. The highest posterior density interval is developed by using Metropolis-Hastings algorithm. Finally, the performances of the different methods have been compared through a Monte Carlo simulation study. The application to set of real data is also analyzed using proposed methods.</p></abstract>

scholarly journals Comparing Mingoti and Glória's and Niverthi and Dey's multivariate capability indexes

Production ◽  
2008 ◽  
Vol 18 (3) ◽  
pp. 598-608 ◽  
Author(s):  
Sueli Aparecida Mingoti ◽  
Fernando Augusto Alves Glória
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Confidence Intervals ◽  
Capability Index ◽  
Bootstrap Methodology

In this paper a comparison between Mingoti and Glória's (2003) and Niverthi and Dey's (2000) multivariate capability indexes is presented. Monte Carlo simulation is used for the comparison and some confidence intervals were generated for the true capability index by using bootstrap methodology.

scholarly journals Validation and Measurement Uncertainty Assessment of a Microbiological Method Using Generalized Pivotal Quantity Procedure and Monte-Carlo Simulation

2018 ◽  
Vol 101 (4) ◽  
pp. 1205-1211
Author(s):  
Saad Alaoui Sossé ◽  
Taoufiq Saffaj ◽  
Bouchaib Ihssane
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Measurement Uncertainty ◽  
Uncertainty Assessment ◽  
Tolerance Interval ◽  
Alternative Procedure ◽  
Pivotal Quantity ◽  
Statistical Tool ◽  
Generalized Pivotal Quantity ◽  
Escherichia Coli Bacteria

Abstract Recently, a novel and effective statistical tool called the uncertainty profile has been developed with the purpose of graphically assessing the validity and estimating the measurement uncertainty of analytical procedures. One way to construct the uncertainty profile is to compute the β-content, γ-confidence tolerance interval. In this study, we propose a tolerance interval based on the combination of the generalized pivotal quantity procedure and Monte-Carlo simulation. The uncertainty profile has been applied successfully in several fields. However, in order to further confirm its universality, this newer approach has been applied to assess the performance of an alternative procedure versus a reference procedure for counting of Escherichia coli bacteria in drinking water. Hence, the aims of this research were to expose how the uncertainty profile can be powerfully applied pursuant to ISO 16140 standards in the frame of interlaboratory study and how to easily make a decision concerning the validity of the procedure. The analysis of the results shows that after the introduction of a correction factor, the alternative procedure is deemed valid over the studied range because the uncertainty limits lie within the acceptability limits set at ±−0.3 log unit/100 ml for a β = 66.7% and γ = 90%.

Interval estimation of operational availability of tree harvesting machines

1987 ◽  
Vol 17 (11) ◽  
pp. 1451-1454
Author(s):  
C. H. Meng ◽  
S. Z. Tang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Analytical Solutions ◽  
Analytical Approach ◽  
Interval Estimation ◽  
Pulp And Paper ◽  
Point Estimation ◽  
Interval Estimate ◽  
Point Estimates ◽  
The Mean

The Canadian Pulp and Paper Association has defined the operational availability of a piece of logging equipment as A = (T − M − D)/T, where T denotes total scheduled machine hours per day, M denotes maintenance hours per day, and D denotes machine downtime per day. The existing literature on logging machines contains only point estimates of the mean operational availability. This paper propounds interval estimation as a preferable alternative since, unlike point estimation, it provides an indication of the uncertainty involved. Two methods of interval estimation are developed: (i) an analytical approach derived from basic theories and (ii) a Monte Carlo simulation. A detailed example is given to demonstrate the application of both methods to the same logging machine. For situations in which theoretical distributions for downtimes and repair times can be assumed, analytical solutions provide general and exact answers for the interval estimate of machine operational availability. However, if theoretical distributions cannot be reasonably assumed and if the integration involved is difficult, the analytical procedures become difficult. In such cases, operational availability can be approximated by the method of Monte Carlo simulation.

scholarly journals Generalized Performance Measures of X- Control Charts Based on Different Sampling Schemes

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Rashid Mehmood ◽  
Muhammed Hisyam Lee ◽  
Muhammad Riaz ◽  
Iftikhar Ali
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Comparative Analysis ◽  
Performance Measures ◽  
Control Charts ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Sampling Strategies ◽  
Pivotal Quantity ◽  
Sampling Schemes

Different versions of X- control chart structure are available under various ranked set strategies. In these control charts, computation of performance measures was carried out through Monte Carlo simulation method (MCSM). In this article, we have defined a generalized structure of X- control charts under variant sampling strategies followed by derivation of their different performance measures. For the derivation of different performance measures, we have proposed pivotal quantity. For comparative analysis, we have presented results of generalized performance measures by involving numerical method (NM) as computation. We found that values of generalized performance measures based on NM are almost similar to values of performance measures based on MCSM. Also, NM is time efficient and can be considered as an alternative of MCSM.

scholarly journals Interval and Point Estimators for the Location Parameter of the Three-Parameter Lognormal Distribution

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Zhenmin Chen ◽  
Feng Miao
Keyword(s):  
Parameter Estimation ◽  
Lognormal Distribution ◽  
Interval Estimation ◽  
Location Parameter ◽  
Point Estimation ◽  
Large Sample Size ◽  
Estimation Problems ◽  
Point Estimator ◽  
Exact Confidence Intervals ◽  
Point Estimators

The three-parameter lognormal distribution is the extension of the two-parameter lognormal distribution to meet the need of the biological, sociological, and other fields. Numerous research papers have been published for the parameter estimation problems for the lognormal distributions. The inclusion of the location parameter brings in some technical difficulties for the parameter estimation problems, especially for the interval estimation. This paper proposes a method for constructing exact confidence intervals and exact upper confidence limits for the location parameter of the three-parameter lognormal distribution. The point estimation problem is discussed as well. The performance of the point estimator is compared with the maximum likelihood estimator, which is widely used in practice. Simulation result shows that the proposed method is less biased in estimating the location parameter. The large sample size case is discussed in the paper.

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