scholarly journals The Probability of a Confidence Interval Based on Minimal Estimates of the Mean and the Standard Deviation

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Louis M. Houston
Keyword(s):  
Computer Simulation ◽  
Distribution Function ◽  
Standard Deviation ◽  
Confidence Interval ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Sample Standard Deviation ◽  
The Mean

Using two measurements, we produce an estimate of the mean and the sample standard deviation. We construct a confidence interval with these parameters and compute the probability of the confidence interval by using the cumulative distribution function and averaging over the parameters. The probability is in the form of an integral that we compare to a computer simulation.

scholarly journals Statistical Properties of SNR for Compressed Measurements

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yulong Gao ◽  
Yanping Chen ◽  
Linxiao Su
Keyword(s):  
Numerical Simulation ◽  
Signal Processing ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Statistical Characteristics ◽  
Communication Signal ◽  
The Mean ◽  
Simulation Results

Some basic statistical properties of the compressed measurements are investigated. It is well known that the statistical properties are a foundation for analyzing the performance of signal detection and the applications of compressed sensing in communication signal processing. Firstly, we discuss the statistical properties of the compressed signal, the compressed noise, and their corresponding energy. And then, the statistical characteristics of SNR of the compressed measurements are calculated, including the mean and the variance. Finally, probability density function and cumulative distribution function of SNR are derived for the cases of the Gamma distribution and the Gaussian distribution. Numerical simulation results demonstrate the correctness of the theoretical analysis.

scholarly journals Nondecreasing Lower Bound on the Poisson Cumulative Distribution Function for z Standard Deviations Above the Mean

2013 ◽  
Vol 50 (4) ◽  
pp. 909-917
Author(s):  
M. Bondareva
Keyword(s):  
Distribution Function ◽  
Lower Bound ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Step Function ◽  
Cumulative Distribution ◽  
Control Parameters ◽  
Poisson Random Variable ◽  
The Mean ◽  
Standard Deviations

In this paper we discuss a nondecreasing lower bound for the Poisson cumulative distribution function (CDF) at z standard deviations above the mean λ, where z and λ are parameters. This is important because the normal distribution as an approximation for the Poisson CDF may overestimate or underestimate its value. A sharp nondecreasing lower bound in the form of a step function is constructed. As a corollary of the bound's properties, for a given percent α and parameter λ, the minimal z is obtained such that, for any Poisson random variable with the mean greater or equal to λ, its αth percentile is at most z standard deviations above its mean. For Poisson distributed control parameters, the corollary allows simple policies measuring performance in terms of standard deviations from a benchmark.

Gaussian Quadrature GQ Used to Accurately Approximate the Relative Weights of Reserves, Contingent Resources, and Prospective Resources Through A Cumulative Distribution Function

2021 ◽  
Author(s):  
Nefeli Moridis ◽  
W. John Lee ◽  
Wayne Sim ◽  
Thomas Blasingame
Keyword(s):  
Distribution Function ◽  
Standard Deviation ◽  
Cumulative Distribution Function ◽  
Gaussian Quadrature ◽  
Random Variables ◽  
Cumulative Distribution ◽  
Production Data ◽  
Discrete Random Variables ◽  
Percent Difference ◽  
The Relationship

Abstract The objective of this work is to numerically estimate the fraction of Reserves assigned to each Reserves category of the PRMS matrix through a cumulative distribution function. We selected 38 wells from a Permian Basin dataset available to Texas A&M University. Previous work has shown that Swanson's Mean, which relates the Reserves categories through a cdf of a normal distribution, is an inaccurate method to determine the relationship of the Reserves categories with asymmetric distributions. Production data are lognormally distributed, regardless of basin type, thus cannot follow the SM concept. The Gaussian Quadrature (GQ) provides a methodology to accurately estimate the fraction of Reserves that lie in 1P, 2P, and 3P categories – known as the weights. Gaussian Quadrature is a numerical integration method that uses discrete random variables and a distribution that matches the original data. For this work, we associate the lognormal cumulative distribution function (CDF) with a set of discrete random variables that replace the production data, and determine the associated probabilities. The production data for both conventional and unconventional fields are lognormally distributed, thus we expect that this methodology can be implemented in any field. To do this, we performed probabilistic decline curve analysis (DCA) using Arps’ Hyperbolic model and Monte Carlo simulation to obtain the 1P, 2P, and 3P volumes, and calculated the relative weights of each Reserves category. We performed probabilistic rate transient analysis (RTA) using a commercial software to obtain the 1P, 2P, and 3P volumes, and calculated the relative weights of each Reserves category. We implemented the 3-, 5-, and 10-point GQ to obtain the weight and percentiles for each well. Once this was completed, we validated the GQ results by calculating the percent-difference between the probabilistic DCA, RTA, and GQ results. We increase the standard deviation to account for the uncertainty of Contingent and Prospective resources and implemented 3-, 5-, and 10-point GQ to obtain the weight and percentiles for each well. This allows us to also approximate the weights of these volumes to track them through the life of a given project. The probabilistic DCA, RTA and Reserves results indicate that the SM is an inaccurate method for estimating the relative weights of each Reserves category. The 1C, 2C, 3C, and 1U, 2U, and 3U Contingent and Prospective Resources, respectively, are distributed in a similar way but with greater variance, incorporated in the standard deviation. The results show that the GQ is able to capture an accurate representation of the Reserves weights through a lognormal CDF. Based on the proposed results, we believe that the GQ is accurate and can be used to approximate the relationship between the PRMS categories. This relationship will aid in booking Reserves to the SEC because it can be recreated for any field. These distributions of Reserves and resources other than Reserves (ROTR) are important for planning and for resource inventorying. The GQ provides a measure of confidence on the prediction of the Reserves weights because of the low percent difference between the probabilistic DCA, RTA, and GQ weights. This methodology can be implemented in both conventional and unconventional fields.

scholarly journals Detection of Giant pulses from pulsar PSR B0950+08

2012 ◽  
Vol 8 (S291) ◽  
pp. 502-504
Author(s):  
T. V. Smirnova
Keyword(s):  
Distribution Function ◽  
Flux Density ◽  
Power Law ◽  
Pulse Energy ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Maximum Peak ◽  
Giant Pulses ◽  
Peak Flux ◽  
The Mean

AbstractWe investigated pulse intensities of PSR B0950+08 at 112 MHz at various longitudes (phases) and detected very strong pulses exceeding the amplitude of the mean profile by more than one hundred times. The maximum peak flux density of a recorded pulse is 15240 Jy, and the energy of this pulse exceeds the mean pulse energy by a factor of 153. The analysis shows that the cumulative distribution function (CDF) of pulse intensities at the longitudes of the main pulse is described by a piece-wise power law, with a slope changing from n=−1.25 ± 0.04 to n=−1.84 ± 0.07 at I≥600 Jy. The CDF for pulses at the longitudes of the precursor has a power law with n=−1.5 ± 0.1. Detected giant pulses from this pulsar have the same signature as giant pulses of other pulsars.

scholarly journals Have You Seen the Standard Deviation?

2019 ◽  
Vol 3 ◽  
pp. 1-10
Author(s):  
Jyotirmoy Sarkar ◽  
Mamunur Rashid
Keyword(s):  
Standard Deviation ◽  
Cumulative Distribution Function ◽  
Geometric Method ◽  
Cumulative Distribution ◽  
Mean Deviation ◽  
Similar Data ◽  
Tabular Data ◽  
Empirical Cumulative Distribution Function ◽  
Quadratic Transformation ◽  
The Mean

Background: Sarkar and Rashid (2016a) introduced a geometric way to visualize the mean based on either the empirical cumulative distribution function of raw data, or the cumulative histogram of tabular data. Objective: Here, we extend the geometric method to visualize measures of spread such as the mean deviation, the root mean squared deviation and the standard deviation of similar data. Materials and Methods: We utilized elementary high school geometric method and the graph of a quadratic transformation. Results: We obtain concrete depictions of various measures of spread. Conclusion: We anticipate such visualizations will help readers understand, distinguish and remember these concepts.

Nondecreasing Lower Bound on the Poisson Cumulative Distribution Function for z Standard Deviations Above the Mean

2013 ◽  
Vol 50 (04) ◽  
pp. 909-917
Author(s):  
M. Bondareva
Keyword(s):  
Distribution Function ◽  
Lower Bound ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Step Function ◽  
Cumulative Distribution ◽  
Control Parameters ◽  
Poisson Random Variable ◽  
The Mean ◽  
Standard Deviations

In this paper we discuss a nondecreasing lower bound for the Poisson cumulative distribution function (CDF) at z standard deviations above the mean λ, where z and λ are parameters. This is important because the normal distribution as an approximation for the Poisson CDF may overestimate or underestimate its value. A sharp nondecreasing lower bound in the form of a step function is constructed. As a corollary of the bound's properties, for a given percent α and parameter λ, the minimal z is obtained such that, for any Poisson random variable with the mean greater or equal to λ, its αth percentile is at most z standard deviations above its mean. For Poisson distributed control parameters, the corollary allows simple policies measuring performance in terms of standard deviations from a benchmark.

scholarly journals Dependability of the Exemplary Technical System for Assumed Functions of Defect Density

2016 ◽  
Vol 39 (1) ◽  
pp. 151-161
Author(s):  
Sławomir Stępień ◽  
Justyna Grzesik
Keyword(s):  
Distribution Function ◽  
Standard Deviation ◽  
Cumulative Distribution Function ◽  
Defect Density ◽  
Technical System ◽  
Cumulative Distribution ◽  
Distribution Shape ◽  
Calculation Results ◽  
Over Time

Abstract The analysis of structural dependability of technical system, especially determining the change in dependability over time, requires knowledge on density function or the understanding of cumulative distribution function of components belonging to the structure. Based on previously registered data concerning component defect, it is relatively easy to establish the average uptime of component as well as the standard deviation for this time. However, defining distribution shape gives rise to some difficulties. Usually, we do not have the sufficient number of data at our disposal to verify the hypothesis regarding the distribution shape. Due to this fact, it is a common practice, depending on the case under consideration, to apply the function of defect density. However, the question arises: Does the incorrect determination of types of distributions of components leads to the big error of estimation results of dependability and system durability? This article will not respond to this question in whole, but one will conduct a comparison of calculation results for a few cases. The calculations were conducted for the exemplary technical system.

scholarly journals Moments of Distance from a Vertex to a Uniformly Distributed Random Point within Arbitrary Triangles

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Hongjun Li ◽  
Xing Qiu
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Cumulative Distribution Function ◽  
Random Point ◽  
Cumulative Distribution ◽  
Computational Technique ◽  
Probability Density Function Pdf

We study the cumulative distribution function (CDF), probability density function (PDF), and moments of distance between a given vertex and a uniformly distributed random point within a triangle in this work. Based on a computational technique that helps us provide unified formulae of the CDF and PDF for this random distance then we compute its moments of arbitrary orders, based on which the variance and standard deviation can be easily derived. We conduct Monte Carlo simulations under various conditions to check the validity of our theoretical derivations. Our method can be adapted to study the random distances sampled from arbitrary polygons by decomposing them into triangles.

Sign in / Sign up

Export Citation Format

Share Document