scholarly journals A Logistic -Moment-Based Analog for the Tukey -, , , and - System of Distributions

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Todd C. Headrick ◽  
Mohan D. Pant
Keyword(s):  
Monte Carlo ◽  
Standard Error ◽  
Relative Bias ◽  
Relative Standard Error ◽  
Moment Estimators ◽  
Heavy Tailed Distributions ◽  
Relative Standard ◽  
Standard Normal ◽  
Heavy Tailed

This paper introduces a standard logistic L-moment-based system of distributions. The proposed system is an analog to the standard normal conventional moment-based Tukey g-h, g, h, and h-h system of distributions. The system also consists of four classes of distributions and is referred to as (i) asymmetric -, (ii) log-logistic , (iii) symmetric , and (iv) asymmetric -. The system can be used in a variety of settings such as simulation or modeling events—most notably when heavy-tailed distributions are of interest. A procedure is also described for simulating -, , , and - distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that estimates of L-skew, L-kurtosis, and L-correlation associated with the -, , , and - distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias and relative standard error.

scholarly journals A Doubling Method for the Generalized Lambda Distribution

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Todd C. Headrick ◽  
Mohan D. Pant
Keyword(s):  
Monte Carlo ◽  
Pearson Correlation ◽  
Relative Bias ◽  
Simulation Studies ◽  
Generalized Lambda Distribution ◽  
New Family ◽  
Heavy Tailed Distributions ◽  
Moment Estimates ◽  
Doubling Method ◽  
Heavy Tailed

This paper introduces a new family of generalized lambda distributions (GLDs) based on a method of doubling symmetric GLDs. The focus of the development is in the context of L-moments and L-correlation theory. As such, included is the development of a procedure for specifying double GLDs with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as modeling events and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when heavy tailed distributions are of concern.

scholarly journals GENERALIZED SYNTHETIC ESTIMATOR FOR DOMAIN MEAN IN TWO PHASE SAMPLING USING SINGLE AUXILIARY CHARACTER

2019 ◽  
pp. 139-151
Author(s):  
Ashutosh ◽  
B. B. Khare ◽  
S. Khare
Keyword(s):  
Simulation Study ◽  
Standard Error ◽  
Relative Bias ◽  
Relative Standard Error ◽  
Two Phase ◽  
Auxiliary Character ◽  
Relative Standard ◽  
Phase Sampling ◽  
Two Phase Sampling

In this paper, we have proposed a two phase sampling estimator for domain mean using auxiliary character with unknown X a domain mean. Also discussed properties of the proposed estimator for domain mean ps a T ,γ , using auxiliary character. Simulation study of the proposed estimator ps a T ,γ , has been made with conventional ratio synthetic estimator for domain mean ps a T ,−1, using auxiliary character in terms of simulated relative standard error (SRSE) and absolute relative bias (ARB). Simulation study shows that under synthetic assumption proposed estimator is more efficient than conventional ratio synthetic estimator for domain mean using auxiliary character.  

scholarly journals Systematic Sampling for Estimating Harvest-Induced Changes of a Forest Stand

2009 ◽  
Vol 9 (1) ◽  
pp. 39-55
Author(s):  
Dennis Peque ◽  
Keyword(s):  
Sample Size ◽  
Standard Error ◽  
Basal Area ◽  
Systematic Sampling ◽  
Relative Standard Error ◽  
Stem Density ◽  
Relative Standard ◽  
The Individual ◽  
Induced Changes ◽  
Forest District

This study was conducted in Compartment 2012a in Bosinghausen Forest District in Germany covering an area of 5 hectared. Twenty two sampling plots were laid out in the field following systematic sampling design. Results showed that all estimates for all variables (e.g. tree heights, DBH, stem density, basal area and volume) under trees that were marked for cutting have higher relative standard error. This was due to higher dispersion of individual estimates in each plot. On the other hand, the simulation study shows that sampling efficiency can be acheived by increasing the sample size. When more samples are included, the relative standard error becomes low. From this study, it can be concluded that the variability of the estimates were affected by sample size and the variability of individual units in the population or the individual esitmates (in this case, estimates in each plot).

A Counting Method for Measuring the Volumes of Tissue Components in Microscopical Sections

1964 ◽  
Vol s3-105 (72) ◽  
pp. 503-517
Author(s):  
A. DOUGLAS HALLY
Keyword(s):  
Standard Error ◽  
Relative Volume ◽  
Square Lattice ◽  
Relative Standard Error ◽  
Consistent Estimate ◽  
Relative Area ◽  
Counting Method ◽  
Tissue Sections ◽  
Relative Standard ◽  
Random Sections

Several methods are available for estimating the relative volume of a tissue component from a study of tissue sections. These methods are all based on the fact that the mean relative area of a component in a series of random sections through a tissue is a consistent estimate of its relative volume in the whole tissue. Thus the problem is basically one of measuring area in a section, which can be done by the following simple counting method. The method consists of placing a regular pattern of points in the form of a square lattice upon the section image, and counting the number of points over the section N, and over the component n Relative area of component ≑n/N The method also measures absolute ares, and where d is the distance between adjacent points, absolute area of component ≑nd2 This capacity to measure absolute area means that the method is particularly suitable for determining a component which has a low relative volume. The accuracy of the method is influenced by several factors including the size of the grid mesh, and the relative area, shape, and spatial arrangment of the component. With reasonable care the error will not be larger than that of a truly randon system of points, as expressed by the following: relative standard error ≑√(1-p)/√n, where p is the relative area of the component, and the relative standard error (R.S.E.) is S.E./relative area of component. The method is equallyapplicable to either light or electron microscopy. A series of measurements on electron micrographs of rat cardiac muscle revealed a close agreement between the counting method and planimetry. The method is rapid, simple and accurate, and requres no complex apparatus.

scholarly journals An L-Moment-Based Analog for the Schmeiser-Deutsch Class of Distributions

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Todd C. Headrick ◽  
Mohan D. Pant
Keyword(s):  
Monte Carlo ◽  
Relative Bias ◽  
Sample Sizes ◽  
Moment Estimators

This paper characterizes the conventional moment-based Schmeiser-Deutsch (S-D) class of distributions through the method of L-moments. The system can be used in a variety of settings such as simulation or modeling various processes. A procedure is also described for simulating S-D distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that the estimates of L-skew, L-kurtosis, and L-correlation associated with the S-D class of distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias—most notably when sample sizes are small.

Reliability of fetal–infant mortality rates in perinatal periods of risk (PPOR) analysis

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Vito Di Bona
Keyword(s):  
Infant Mortality ◽  
Standard Error ◽  
Infant Mortality Rate ◽  
Relative Standard Error ◽  
Statistical Reliability ◽  
Relative Standard ◽  
Vital Records ◽  
Large Populations ◽  
Perinatal Periods Of Risk ◽  
Interval Estimators

Abstract The Fetal–Infant mortality rate (FIMR) is the basic surveillance statistic in perinatal periods of risk (PPOR) analyses. This paper presents a model for the FIMR as the ratio of two Poisson random variables. From this model, expressions for estimators of variance, standard error, and relative standard error are developed. The coverage properties of interval estimators for the FIMR are investigated in a simulation study for both small and large populations and FIMR rates. Results from these studies are applied to a PPOR analysis of NC vital records. Results suggest that the sample size guidance provided in the literature to ensure statistical reliability is overly conservative and interval construction methodology should be selected based on population size.

scholarly journals Bayesian Estimation of Random Parameter Models of Responses with Normal and Skew-t Distibutions Evidence from Monte Carlo Simulation

2018 ◽  
Vol 24 (1) ◽  
pp. 27-50
Author(s):  
Mohammad Masjkur ◽  
Henk Folmer
Keyword(s):  
Monte Carlo ◽  
Dose Response ◽  
Random Parameter ◽  
Response Models ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Response Modeling ◽  
T Distribution ◽  
Valuation Criteria ◽  
Skew Normal

Random parameter models have been found to outperform xed pa-rameter models to estimate dose-response relationships with independent errors. Amajor restriction, however, is that the responses are assumed to be normally andsymmetrically distributed. The purpose of this paper is to analyze Bayesian infer-ence of random parameter response models in the case of independent responseswith normal and skewed, heavy-tailed distributions by way of Monte Carlo simu-lation. Three types of Bayesian estimators are considered: one applying a normal,symmetrical prior distribution, a second applying a Skew-normal prior and, a thirdapplying a Skew-t-distribution. We use the relative bias (RelBias) and Root MeanSquared Error (RMSE) as valuation criteria. We consider the commonly applied lin-ear Quadratic and the nonlinear Spillman-Mitscherlich dose-response models. Onesimulation examines the performance of the estimators in the case of independent,normally and symmetrically distributed responses; the other in the case of indepen-dent responses following a heavy-tailed, Skew-t-distribution. The main nding isthat the estimator based on the Skew-t prior outperforms the alternative estima-tors applying the normal and Skew-normal prior for skewed, heavy-tailed data. Fornormal data, the Skew-t prior performs approximately equally well as the Skew-normal and the normal prior. Furthermore, it is more ecient than its alternatives.Overall, the Skew-t prior seems to be preferable to the normal and Skew-normal fordose-response modeling.

Kinetic Method for the Determination of 2,4-Dinitrophenol

2008 ◽  
Vol 59 (7) ◽  
Author(s):  
S. S. Mitic ◽  
V. V. Zivanovic ◽  
G. Z. Miletic ◽  
D. A. Kostic ◽  
I. D. Rasic
Keyword(s):  
Detection Limit ◽  
River Water ◽  
Standard Error ◽  
Kinetic Method ◽  
Relative Standard Error ◽  
Potassium Periodate ◽  
Experimental Conditions ◽  
Inhibiting Effect ◽  
Relative Standard

A kinetic method for the determination of dinitrophenol is proposed. The method is based on the inhibiting effect of 2,4-dinitrophenol on the Mn(II) catalysis of the oxidation of malachite green with potassium periodate. The reaction was monitored spectrophotometrically at 615 nm. Kinetic expressions for the reaction are postulated. The optimal experimental conditions for the determination of 2,4-dinitrophenol were established and 2,4-dinitrophenol was determined in concentrations from 0.092-0.92 mg . mL-1 with relative standard error of 5.9 %. Detection limit is 0.014 mg . mL-1. The selectivity of the method is appropriate. The method was applied for the determination of dinitrophenol in urine and river water.

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