NONPARAMETRIC KERNEL DISTRIBUTION FUNCTION ESTIMATION NEAR ENDPOINTS

2021 ◽  
Vol 10 (12) ◽  
pp. 3679-3697
Author(s):  
N. Almi ◽  
A. Sayah
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Kernel Estimator ◽  
Real Data ◽  
Cumulative Distribution ◽  
Function Estimation ◽  
Distribution Function Estimation ◽  
The Right ◽  
Nonparametric Kernel ◽  
Better Than

In this paper, two kernel cumulative distribution function estimators are introduced and investigated in order to improve the boundary effects, we will restrict our attention to the right boundary. The first estimator uses a self-elimination between modify theoretical Bias term and the classical kernel estimator itself. The basic technique of construction the second estimator is kind of a generalized reflection method involving reflection a transformation of the observed data. The theoretical properties of our estimators turned out that the Bias has been reduced to the second power of the bandwidth, simulation studies and two real data applications were carried out to check these phenomena and are conducted that the proposed estimators are better than the existing boundary correction methods.

scholarly journals Ground Clutter as a Monitor of Radar Stability at Kwajalein, RMI

2008 ◽  
Vol 25 (11) ◽  
pp. 2037-2045 ◽  
Author(s):  
David S. Silberstein ◽  
David B. Wolff ◽  
David A. Marks ◽  
David Atlas ◽  
Jason L. Pippitt
Keyword(s):  
Distribution Function ◽  
Solar Radiation ◽  
Cumulative Distribution Function ◽  
Tropical Rainfall Measuring Mission ◽  
Daily Basis ◽  
Cumulative Distribution ◽  
Equipment Failure ◽  
Ground Clutter ◽  
Radar Measurements ◽  
Better Than

Abstract There are many applications in which the absolute and day-to-day calibrations of radar sensitivity are necessary. This is particularly so in the case of quantitative radar measurements of precipitation. While fine calibrations may be made periodically by a variety of techniques such as the use of antenna ranges, standard targets, and solar radiation, knowledge of variations that occur between such checks is required to maintain the accuracy of the data. This paper presents a method for this purpose using the radar on Kwajalein Atoll to provide a baseline calibration for the control of measurements of rainfall made by the Tropical Rainfall Measuring Mission (TRMM). The method uses echoes from a multiplicity of ground targets. The daily average clutter echoes at the lowest elevation scan have been found to be remarkably stable from hour to hour, day to day, and month to month within better than ±1 dB. They vary significantly only after either deliberate system modifications, equipment failure, or other unknown causes. A cumulative distribution function (CDF) of combined precipitation and clutter reflectivity (Ze in dBZ) is obtained on a daily basis, regardless of whether or not rain occurs over the clutter areas. The technique performs successfully if the average daily area mean precipitation echoes (over the area of the clutter echoes) do not exceed 45 dBZ, a condition that is satisfied in most locales. In comparison, reflectivities associated with the most intense clutter echoes can approach 70 dBZ. Thus, the level at which the CDF reaches 95% is affected only by the clutter and reflects variations only in the radar sensitivity. Daily calculations of the CDFs have recently been made beginning with August 1999 data and are used to correct 7.5 yr of measurements, thus enhancing the integrity of the global record of precipitation observed by TRMM. The method is robust and may be applicable to other ground-based radars.

The joint asymptotic distribution of the k-smallest sample spacings

1969 ◽  
Vol 6 (02) ◽  
pp. 442-448
Author(s):  
Lionel Weiss
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Open Interval ◽  
Cumulative Distribution ◽  
The Right ◽  
Sample Spacings ◽  
Independent Identically Distributed

Suppose Q 1 ⋆, … Q n ⋆ are independent, identically distributed random variables, each with probability density function f(x), cumulative distribution function F(x), where F(1) – F(0) = 1, f(x) is continuous in the open interval (0, 1) and continuous on the right at x = 0 and on the left at x = 1, and there exists a positive C such that f(x) > C for all x in (0, l). f(0) is defined as f(0+), f(1) is defined as f(1–).

A Simplification and Implementation of Random-effects Meta-analyses Based on the Exact Distribution of Cochran’s Q

2014 ◽  
Vol 53 (01) ◽  
pp. 54-61 ◽  
Author(s):  
M. Preuß ◽  
A. Ziegler
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Type I Error ◽  
Meta Analysis ◽  
Real Data ◽  
R Package ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Type I ◽  
Simulation Studies

SummaryBackground: The random-effects (RE) model is the standard choice for meta-analysis in the presence of heterogeneity, and the stand ard RE method is the DerSimonian and Laird (DSL) approach, where the degree of heterogeneity is estimated using a moment-estimator. The DSL approach does not take into account the variability of the estimated heterogeneity variance in the estimation of Cochran’s Q. Biggerstaff and Jackson derived the exact cumulative distribution function (CDF) of Q to account for the variability of Ť 2.Objectives: The first objective is to show that the explicit numerical computation of the density function of Cochran’s Q is not required. The second objective is to develop an R package with the possibility to easily calculate the classical RE method and the new exact RE method.Methods: The novel approach was validated in extensive simulation studies. The different approaches used in the simulation studies, including the exact weights RE meta-analysis, the I 2 and T 2 estimates together with their confidence intervals were implemented in the R package metaxa.Results: The comparison with the classical DSL method showed that the exact weights RE meta-analysis kept the nominal type I error level better and that it had greater power in case of many small studies and a single large study. The Hedges RE approach had inflated type I error levels. Another advantage of the exact weights RE meta-analysis is that an exact confidence interval for T 2is readily available. The exact weights RE approach had greater power in case of few studies, while the restricted maximum likelihood (REML) approach was superior in case of a large number of studies. Differences between the exact weights RE meta-analysis and the DSL approach were observed in the re-analysis of real data sets. Application of the exact weights RE meta-analysis, REML, and the DSL approach to real data sets showed that conclusions between these methods differed.Conclusions: The simplification does not require the calculation of the density of Cochran’s Q, but only the calculation of the cumulative distribution function, while the previous approach required the computation of both the density and the cumulative distribution function. It thus reduces computation time, improves numerical stability, and reduces the approximation error in meta-analysis. The different approaches, including the exact weights RE meta-analysis, the I 2 and T 2estimates together with their confidence intervals are available in the R package metaxa, which can be used in applications.

scholarly journals A New Kernel Estimator of Copulas Based on Beta Quantile Transformations

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1078
Author(s):  
Catalina Bolancé ◽  
Carlos Alberto Acuña
Keyword(s):  
Distribution Function ◽  
Data Analysis ◽  
Simulation Study ◽  
Financial Risk ◽  
Cumulative Distribution Function ◽  
Kernel Estimator ◽  
Cumulative Distribution ◽  
Nonparametric Estimator ◽  
Marginal Distributions ◽  
Kernel Approach

A copula is a multivariate cumulative distribution function with marginal distributions Uniform(0,1). For this reason, a classical kernel estimator does not work and this estimator needs to be corrected at boundaries, which increases the difficulty of the estimation and, in practice, the bias boundary correction might not provide the desired improvement. A quantile transformation of marginals is a way to improve the classical kernel approach. This paper shows a Beta quantile transformation to be optimal and analyses a kernel estimator based on this transformation. Furthermore, the basic properties that allow the new estimator to be used for inference on extreme value copulas are tested. The results of a simulation study show how the new nonparametric estimator improves alternative kernel estimators of copulas. We illustrate our proposal with a financial risk data analysis.

scholarly journals An Asymmetric Bimodal Distribution with Application to Quantile Regression

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 899 ◽  
Author(s):  
Yolanda M. Gómez ◽  
Emilio Gómez-Déniz ◽  
Osvaldo Venegas ◽  
Diego I. Gallardo ◽  
Héctor W. Gómez
Keyword(s):  
Distribution Function ◽  
Maximum Likelihood ◽  
Quantile Regression ◽  
Simulation Study ◽  
Cumulative Distribution Function ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Bimodal Distribution ◽  
Cumulative Distribution ◽  
Cauchy Model

In this article, we study an extension of the sinh Cauchy model in order to obtain asymmetric bimodality. The behavior of the distribution may be either unimodal or bimodal. We calculate its cumulative distribution function and use it to carry out quantile regression. We calculate the maximum likelihood estimators and carry out a simulation study. Two applications are analyzed based on real data to illustrate the flexibility of the distribution for modeling unimodal and bimodal data.

The joint asymptotic distribution of the k-smallest sample spacings

1969 ◽  
Vol 6 (2) ◽  
pp. 442-448 ◽  
Author(s):  
Lionel Weiss
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Open Interval ◽  
Cumulative Distribution ◽  
The Right ◽  
Sample Spacings ◽  
Independent Identically Distributed

Suppose Q1⋆, … Qn⋆ are independent, identically distributed random variables, each with probability density function f(x), cumulative distribution function F(x), where F(1) – F(0) = 1, f(x) is continuous in the open interval (0, 1) and continuous on the right at x = 0 and on the left at x = 1, and there exists a positive C such that f(x) > C for all x in (0, l). f(0) is defined as f(0+), f(1) is defined as f(1–).

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