On Some Finite Range Life Distributions

2017 ◽  
Vol 69 (1) ◽  
pp. 103-109
Author(s):  
S. P. Mukherjee
Keyword(s):  
Shape Parameter ◽  
Probability Distributions ◽  
Finite Range ◽  
Shape Parameters ◽  
Bhattacharyya Distance ◽  
Independent Components ◽  
A Value ◽  
Rectangular Distribution ◽  
Life Distributions ◽  
Parameter Values

Various reliability properties, including some characterization results, have been investigated for two finite range life distributions. One of these, namely, the exponentiated rectangular distribution, exhibits a bath-tub failure rate when the shape parameter has a value less than unity and, as expected, does not conform to certain results relating to ageing properties, which hold in the case of distributions with monotone failure rates. Moments as well as best percentile estimates of the shape parameter for this distribution have been worked out. Stress–strength reliability when stress and strength follow the same distribution of this type over the same range, but with different shape parameter values, has been derived and shown to be related to the Bhattacharyya distance between the two probability distributions. Distributions of parallel and standby system lives for two independent components, with this distribution having varying shape parameters, have been derived.

scholarly journals Local Convexity-PreservingC2Rational Cubic Spline for Convex Data

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammad Abbas ◽  
Ahmad Abd Majid ◽  
Jamaludin Md. Ali
Keyword(s):  
Shape Parameter ◽  
Cubic Spline ◽  
Convex Curve ◽  
Shape Feature ◽  
Local Convexity ◽  
Shape Parameters ◽  
Numerical Examples ◽  
2D Data ◽  
Industrial Demand ◽  
Made In

We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data usingC2rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing.

Accounting For Corrosion Of Hlw Glasses By Humid Air In TSPA

2002 ◽  
Vol 757 ◽  
Author(s):  
W. L. Ebert ◽  
J. C. Cunnane ◽  
N. L. Dietz
Keyword(s):  
Rate Equation ◽  
Ph Dependence ◽  
Yucca Mountain ◽  
Total System ◽  
Humid Air ◽  
Determine Parameter ◽  
Glass Dissolution ◽  
A Value ◽  
License Application ◽  
Parameter Values

ABSTRACTThis paper describes how the results of vapor hydration tests (VHTs) are used to model the corrosion of waste glasses exposed to humid air in the glass degradation model for total system performance assessment (TSPA) calculations for the proposed Yucca Mountain disposal system. Corrosion rates measured in VHTs conducted at 125, 150, 175, and 200°C are compared with the rate equation for aqueous dissolution to determine parameter values that are applicable to glass degradation in humid air. These will be used to determine the minimum for the range and distribution of parameter values in calculations for the Yucca Mountain disposal system license application (TSPA-LA). The rate equation for glass dissolution is rate = kE • 10 η • pH • exp(–Ea/RT). Uncertainties in the calculated rate due to the range of waste glass compositions and water exposure conditions are taken into account by using a range of values for the rate coefficient kE. The parameter values for the pH dependence (η) and temperature dependence (Ea) and the upper limit for kE are being determined with other tests. Using the values of η and Ea from the site recommendation model, the VHT results described in this paper provide a value of log kE = 5.1 as the minimum value for the rate expression. This value will change slightly if different pH-and temperature-dependencies are used for the TSPA-LA model.

scholarly journals A Note on Ordering Probability Distributions by Skewness

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 286
Author(s):  
V. García ◽  
M. Martel-Escobar ◽  
F. Vázquez-Polo
Keyword(s):  
Data Analysis ◽  
Probability Distributions ◽  
Continuous Distributions ◽  
Parameter Values

This paper describes a complementary tool for fitting probabilistic distributions in data analysis. First, we examine the well known bivariate index of skewness and the aggregate skewness function, and then introduce orderings of the skewness of probability distributions. Using an example, we highlight the advantages of this approach and then present results for these orderings in common uniparametric families of continuous distributions, showing that the orderings are well suited to the intuitive conception of skewness and, moreover, that the skewness can be controlled via the parameter values.

scholarly journals Archie's law – a reappraisal

Solid Earth ◽  
2016 ◽  
Vol 7 (4) ◽  
pp. 1157-1169 ◽  
Author(s):  
Paul W. J. Glover
Keyword(s):  
Systematic Errors ◽  
Apparent Paradox ◽  
Archie’S Law ◽  
A Value ◽  
The Difference ◽  
Reservoir Parameter ◽  
Parameter Values ◽  
Electrical Data ◽  
Extra Parameter ◽  
Better Than

Abstract. When scientists apply Archie's first law they often include an extra parameter a, which was introduced about 10 years after the equation's first publication by Winsauer et al. (1952), and which is sometimes called the “tortuosity” or “lithology” parameter. This parameter is not, however, theoretically justified. Paradoxically, the Winsauer et al. (1952) form of Archie's law often performs better than the original, more theoretically correct version. The difference in the cementation exponent calculated from these two forms of Archie's law is important, and can lead to a misestimation of reserves by at least 20 % for typical reservoir parameter values. We have examined the apparent paradox, and conclude that while the theoretical form of the law is correct, the data that we have been analysing with Archie's law have been in error. There are at least three types of systematic error that are present in most measurements: (i) a porosity error, (ii) a pore fluid salinity error, and (iii) a temperature error. Each of these systematic errors is sufficient to ensure that a non-unity value of the parameter a is required in order to fit the electrical data well. Fortunately, the inclusion of this parameter in the fit has compensated for the presence of the systematic errors in the electrical and porosity data, leading to a value of cementation exponent that is correct. The exceptions are those cementation exponents that have been calculated for individual core plugs. We make a number of recommendations for reducing the systematic errors that contribute to the problem and suggest that the value of the parameter a may now be used as an indication of data quality.

scholarly journals Probability distributions of COVID-19 tweet posted trends use a nonhomogeneous Poisson process

2020 ◽  
Vol 1 (4) ◽  
pp. 229-238
Author(s):  
Devi Munandar ◽  
Sudradjat Supian ◽  
Subiyanto Subiyanto
Keyword(s):  
Social Media ◽  
Poisson Process ◽  
Exponential Distribution ◽  
Probability Distributions ◽  
Nonhomogeneous Poisson Process ◽  
Time Interval ◽  
Initial State ◽  
Time Intervals ◽  
Time Parameters ◽  
Parameter Values

The influence of social media in disseminating information, especially during the COVID-19 pandemic, can be observed with time interval, so that the probability of number of tweets discussed by netizens on social media can be observed. The nonhomogeneous Poisson process (NHPP) is a Poisson process dependent on time parameters and the exponential distribution having unequal parameter values and, independently of each other. The probability of no occurrence an event in the initial state is one and the probability of an event in initial state is zero. Using of non-homogeneous Poisson in this paper aims to predict and count the number of tweet posts with the keyword coronavirus, COVID-19 with set time intervals every day. Posting of tweets from one time each day to the next do not affect each other and the number of tweets is not the same. The dataset used in this study is crawling of COVID-19 tweets three times a day with duration of 20 minutes each crawled for 13 days or 39 time intervals. The result of this study obtained predictions and calculated for the probability of the number of tweets for the tendency of netizens to post on the situation of the COVID-19 pandemic.

scholarly journals Moment based Estimation for the Shape Parameters, Effect it on Some Probability Statistical Distributions Using the Moment Method and Maximum Likelihood Method

2020 ◽  
Vol 5 (6) ◽  
pp. 979-986
Author(s):  
Hassan Tawakol A. Fadol
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Likelihood Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Best Estimate

The purpose of this paper was to identify the values of the parameters of the shape of the binomial, bias one and natural distributions. Using the estimation method and maximum likelihood Method, the criterion of differentiation was used to estimate the shape parameter between the probability distributions and to arrive at the best estimate of the parameter of the shape when the sample sizes are small, medium, The problem was to find the best estimate of the characteristics of the society to be estimated so that they are close to the estimated average of the mean error squares and also the effect of the estimation method on estimating the shape parameter of the distributions at the sizes of different samples In the values of the different shape parameter, the descriptive and inductive method was selected in the analysis of the data by generating 1000 random numbers of different sizes using the simulation method through the MATLAB program. A number of results were reached, 10) to estimate the small shape parameter (0.3) for binomial distributions and Poisson and natural and they can use the Poisson distribution because it is the best among the distributions, and to estimate the parameter of figure (0.5), (0.7), (0.9) Because it is better for binomial binomial distributions, when the size of a sample (70) for a teacher estimate The small figure (0.3) of the binomial and boson distributions and natural distributions can be used for normal distribution because it is the best among the distributions.

scholarly journals PENGARUH PERUBAHAN NILAI PARAMETER TERHADAP NILAI ERROR PADA METODE RUNGE-KUTTA ORDE 3

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Tornados P Silaban ◽  
Faiz . Ahyaningsih
Keyword(s):  
Linear Equations ◽  
Research Process ◽  
Kutta Method ◽  
System Of Linear Equations ◽  
Runge Kutta Method ◽  
A Value ◽  
Fixed Parameter ◽  
Higher Derivatives ◽  
Runge Kutta ◽  
Parameter Values

ABSTRACTRunge-Kutta method is a numerical method used to find the solution of an equation. This method seeks to obtain a higher degree of precision, and at the same time seeking to avoid the need of higher derivatives by evaluating the function f (x, y) at the selected point in each interval step. In this paper discussed the effect of changes in the value of the parameter (h) to the value of the error in the Runge-Kutta method Order-3. The equation to be discussed is a linear ordinary differential equation of the two levels that have been changed into a system of linear equations. In the research process was not found fixed parameter values to get the minimum error value, because each parameter has a value of error varied for each equation.Keywords: Runge-Kutta, parameters, error.

A Simple Method for Estimating the Parameters of the Beta Distribution Applied to Modeling Uncertainty in Gas Turbine Inlet Temperature

2002 ◽  
Author(s):  
Frederic A. Holland
Keyword(s):  
Standard Deviation ◽  
Conventional Method ◽  
Beta Distribution ◽  
Conventional Approach ◽  
Algebraic Solution ◽  
Inlet Temperature ◽  
Shape Parameters ◽  
Simple Method ◽  
New Approach ◽  
A Value

The beta distribution is a particularly convenient model for random variables when only the minimum, maximum and most likely values are available. It is also very useful for estimating the mean and standard deviation given this information. In this paper a simple method is proposed to estimate the beta parameters from these three values. The proposed method has advantages over the conventional approach. In the conventional approach, the four parameters of the beta distribution are determined from only three values by assuming a standard deviation that is one-sixth the range. In contrast, the new method assumes a value for one of the beta shape parameters based on an analogy with the normal distribution. This new approach allows for a very simple algebraic solution of the beta shape parameters in contrast to the simultaneous solution required by the conventional method. The results of the proposed method are very similar to the conventional method. However, the proposed method generally gives a slightly higher (more conservative) estimate of the standard deviation when the distribution is skewed. In addition, the new approach allows the standard deviation to vary as the shape or skew of the distribution varies. Both methods were applied to modeling the probability distribution of temperature.

On a Generating Function and its Probability Distributions. A Contribution to the Theory of Transition Rates I

2006 ◽  
Vol 61 (9) ◽  
pp. 457-468
Author(s):  
Hans Kupka
Keyword(s):  
Probability Distribution ◽  
Generating Function ◽  
Probability Distributions ◽  
Addition Theorem ◽  
Complex Variables ◽  
Transition Rates ◽  
Multidimensional Distribution ◽  
Multiple Peak ◽  
Integer Variables ◽  
A Value

A function of two complex variables with two real parameters a and b is described, which generates a sequence of probability distributions of two integer variables m ≥ 0 and n ≥ 0. Closed expressions for the special b = 0 and general case b≠ 0 and recurrence equations for calculating the probability distributions are derived. The probability distribution for m = 0 and a large enough is qualitatively bell-shaped, and that for m ≠ 0 has multiple peak structures. In both cases, the b parameter influences solely the skewness of the curves. For small a values, the distributions fall rapidly from a value of nearly one, decreasing by a factor of 1010 or more as n increases from zero to n = 10. The influence of the b parameter on their properties can be pronounced. Finally, we note an important property of the distributions when two or several of them are convoluted with one another. The result is expressed in terms of an addition theorem in respect to the parameter a and describes a multidimensional distribution.

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