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.

scholarly journals Multistage Estimation of the Rayleigh Distribution Variance

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2084
Author(s):  
Ali Yousef ◽  
Ayman A. Amin ◽  
Emad E. Hassan ◽  
Hosny I. Hamdy
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Interval Estimation ◽  
Sequential Estimation ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Asymptotic Results ◽  
Squared Error Loss Function ◽  
Estimation Problems ◽  
Width Confidence Interval

In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh distribution’s scale parameter’s square. We tackle two estimation problems: first, the minimum risk point estimation problem under a squared-error loss function plus linear sampling cost, and the second is a fixed-width confidence interval estimation, using a unified optimal stopping rule. Such an estimation cannot be performed using fixed-width classical procedures due to the non-existence of a fixed sample size that simultaneously achieves both estimation problems. We find all the asymptotic results that enhanced finding the three-stage regret as well as the three-stage fixed-width confidence interval for the desired parameter. The procedure attains asymptotic second-order efficiency and asymptotic consistency. A series of Monte Carlo simulations were conducted to study the procedure’s performance as the optimal sample size increases. We found that the simulation results agree with the asymptotic results.

scholarly journals Sequential point and interval estimation of scale parameter of exponential distribution

1995 ◽  
Vol 18 (2) ◽  
pp. 383-390
Author(s):  
Z. Govindarajulu
Keyword(s):  
Exponential Distribution ◽  
Scale Parameter ◽  
Stopping Time ◽  
Interval Estimation ◽  
Location Parameter ◽  
Exact Expression ◽  
Point Estimation ◽  
Quadratic Loss ◽  
Negative Exponential Distribution ◽  
Negative Exponential

Sequential fixed-width confidence intervals are obtained for the scale parameterσwhen the location parameterθof the negative exponential distribution is unknown. Exact expressions for the stopping time and the confidence coefficient associated with the sequential fixed-width interval are derived. Also derived is the exact expression for the stopping time of sequential point estimation with quadratic loss and linear cost. These are numerically evaluated for certain nominal confidence coefficients, widths of the interval and cost functions, and are compared with the second order asymptotic expressions.

Unpredictable Voters in Ideal Point Estimation

2010 ◽  
Vol 18 (2) ◽  
pp. 151-171 ◽  
Author(s):  
Benjamin E. Lauderdale
Keyword(s):  
Voting Behavior ◽  
Ideal Point ◽  
Error Variance ◽  
Point Estimation ◽  
Point Estimator ◽  
Ideal Points ◽  
Variance Parameters ◽  
Point Estimators ◽  
Low Dimensional ◽  
Specific Error

Ideal point estimators are typically based on an assumption that all legislators are equally responsive to modeled dimensions of legislative disagreement; however, particularistic constituency interests and idiosyncrasies of individual legislators introduce variation in the degree to which legislators cast votes predictably. I introduce a Bayesian heteroskedastic ideal point estimator and demonstrate by Monte Carlo simulation that it outperforms standard homoskedastic estimators at recovering the relative positions of legislators. In addition to providing a refinement of ideal point estimates, the heteroskedastic estimator recovers legislator-specific error variance parameters that describe the extent to which each legislator's voting behavior is not conditioned on the primary axes of disagreement in the legislature. Through applications to the roll call histories of the U.S. Congress, the E.U. Parliament, and the U.N. General Assembly, I demonstrate how to use the heteroskedastic estimator to study substantive questions related to legislative incentives for low-dimensional voting behavior as well as diagnose unmodeled dimensions and nonconstant ideal points.

OBTAINING POINT ESTIMATORS OF PARAMETERS FROM CONFIDENCE INTERVALS OR JOINT CONFIDENCE REGIONS

2007 ◽  
Vol 14 (01) ◽  
pp. 21-28
Author(s):  
ZHENMIN CHEN
Keyword(s):  
Maximum Likelihood ◽  
Population Distribution ◽  
Confidence Region ◽  
Interval Estimation ◽  
Likelihood Estimation ◽  
Confidence Regions ◽  
Point Estimation ◽  
Estimation Of Parameters ◽  
Unknown Parameters ◽  
Point Estimators

There are several different ways to obtain point estimators for the parameters of a population distribution. The maximum likelihood estimation and moment estimation are the most commonly used ones. Using point estimators only to estimate unknown parameters is somewhat risky because the probability that the estimation is wrong is almost 100%. Interval estimation, on the other hand, can reduce this risk considerably. The purpose of this paper is to propose a new method for obtaining point estimation of parameters. The point estimators discussed here are obtained by squeezing a confidence interval or joint confidence region of the parameters. The proposed method is easy to use in some cases. The estimators obtained by using this method possess some unbiasedness property. It is also shown that the point estimator obtained by this method is more reasonable than the maximum likelihood estimator when the population distribution is skewed.

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.

Decoupled Location Parameter Estimation of Near-Field Sources with Symmetric ULA

2011 ◽  
Vol E94-B (9) ◽  
pp. 2646-2649
Author(s):  
Bum-Soo KWON ◽  
Tae-Jin JUNG ◽  
Kyun-Kyung LEE
Keyword(s):  
Parameter Estimation ◽  
Near Field ◽  
Location Parameter

scholarly journals Set-membership identifiability of nonlinear models and related parameter estimation properties

2016 ◽  
Vol 26 (4) ◽  
pp. 803-813 ◽  
Author(s):  
Carine Jauberthie ◽  
Louise Travé-MassuyèEs ◽  
Nathalie Verdière
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Dynamic System ◽  
Nonlinear Models ◽  
Differential Algebra ◽  
Related Parameter ◽  
Set Membership ◽  
Estimation Problems ◽  
The Mathematical Model

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

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