• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.437-443
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• 2008

In this paper, we establish detailed characterizations of the Weibull distribution by the independence of the upper record values. We prove that X $\in$ W EI($\alpha$), if and only if $\frac{X_{U(n)}}{X_{U(n+1)}+X_{U(n)}}$ and $X_{U(n+1)}$ are independent for n $\geq$ 1. And we show that X $\in$ W EI($\alpha$), if and only if $\frac{X_{U(n+1)}-X_{U(n)}}{X_{U(n+1)}+X_{U(n)}}$ and $X_{U(n+1)}$ are independent for n $\geq$ 1.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1435-1451
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• 2011

In this paper the estimation of the parameters as well as survival and hazard functions are presented for the two-parameter Pareto distribution by using Bayesian and non-Bayesian approaches under upper record values. Maximum likelihood estimation (MLE) and interval estimation are derived for the parameters. Bayes estimators of reliability performances are obtained under symmetric (Squared error) and asymmetric (Linex and general entropy (GE)) losses, when two parameters have discrete and continuous priors, respectively. Finally, two numerical examples with real data set and simulated data, are presented to illustrate the proposed method. An algorithm is introduced to generate records data, then a simulation study is performed and different estimates results are compared.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1249-1257
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• 2012

In this paper, we derive maximum likelihood estimators (MLEs) and approximate MLEs (AMLEs) of the unknown parameters in a generalized half logistic distribution when the data are upper record values. As an illustration, we examine the validity of our estimation using real data and simulated data. Finally, we compare the proposed estimators in the sense of the mean squared error (MSE) through a Monte Carlo simulation for various record values of size.

• Magazine of the Korean Society of Agricultural Engineers
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• v.23 no.2
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• pp.45-53
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• 1981

Long term precipitation gaging station record (58 years) was analyzed by progressive mean method to compare the estimated effective period of records for computing mean and probable values. Obtained results are as follows: 1. Fifty-eight years precipitation records at Jinju, Gyeong Sang Nam Do was analyzed by double mass analysis method. Result was appeared that the record was consistent with time. 2. The effective period of records for estimating mean values with the departure of 5% or less from the true mean are up to 33 years for annual precipitation, 20 years for annual maximum daily precipitation and 45 years for maximum successive dry days in summer season. 3. To estimate the probable values by Gumbel-Chow method within the departure of 5% level from true value, periods of 51 years, 38 years and 45 years were required for annual precipitation, annual maximum daily precipitation and maximum successive dry days in summer season, respectively.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.163-167
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• 2008

This paper presents characterizations of the Weibull distribution by the independence of record values. We prove that $X\;{\in}\;W\;EI ({\alpha})$, if and only if $\frac {X_{U(n+l)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent or $\frac {X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent. And also we establish that $X\;{\in}\;W\;EI({\alpha})$, if and only if $\frac {X_{U(n+1)}\;-\;X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.85-89
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• 2011

We present characterizations of the Pareto distribution by the independent property of upper record values in such a way that F(x) has a Pareto distribution if and only if $\frac{X_{U(n)}}{X_{U(m)}}$ and $X_{U(m)}$ are independent for $1{\leq}m. Futhermore, the characterizations should find that F(x) has a Pareto distribution if and only if $\frac{X_{U(n)}}{X_{U(n)}{\pm}X_{U(m)}}$ and $X_{U(m)}$ are independent for $1{\leq}m.

• Communications for Statistical Applications and Methods
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• v.31 no.5
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• pp.497-519
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• 2024

In reliability analysis, the probability P(Y < X) is significant because it denotes availability and dependability in a stress-strength model where Y and X are the stress and strength variables, respectively. In reliability theory, the inverse Lomax distribution is a well-established lifetime model, and the literature is developing inference techniques for its reliability attributes. In this article, we are interested in estimating the stress-strength reliability R = P(Y < X), where X and Y have an unknown common scale parameter and follow the inverse Lomax distribution. Using Bayesian and non-Bayesian approaches, we discuss this issue when both stress and strength are expressed in terms of lower record values. The parametric bootstrapping techniques of R are taken into consideration. The stress-strength reliability estimator is investigated using uniform and gamma priors with several loss functions. Based on the proposed loss functions, the reliability R is estimated using Bayesian analyses with Gibbs and Metropolis-Hasting samplers. Monte Carlo simulation studies and real-data-based examples are also performed to analyze the behavior of the proposed estimators. We analyze electrical insulating fluids, particularly those used in transformers, for data sets using the stress-strength model. In conclusion, as expected, the study's results showed that the mean squared error values decreased as the record number increased. In most cases, Bayesian estimates under the precautionary loss function are more suitable in terms of simulation conclusions than other specified loss functions.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.97-102
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the Pareto distribution. Let ｛$X_n,n\qeq1$｝be a sequence of independent and identically distributed random variables with a common continuous distribution function(cdf) F($chi$) and probability density function(pdf) f($chi$). Let $Y_n\;=\;mas{X_1,X_2,...,X_n}$ for $ngeq1$. We say $X_{j}$ is an upper record value of {$X_{n},n\geq1$}, if $Y_{j}$＞$Y_{j-1}$,j＞1. The indices at which the upper record values occur are given by the record times ${u( n)}n,\geq1$, where u(n) = min{j｜j ＞u(n-l), $X_{j}$＞$X_{u(n-1)}$,n\qeq2$ and u(l) = 1. Suppose $X{\epsilon}PAR(\frac{1}{\beta},\frac{1}{\beta}$ then E$(\frac{{X^\tau}}_{u(m)}}{{X^{s+1}}_{u(n)})\;=\;\frac{1}{s}E$ E$(\frac{{X^\tau}}_{u(m)}{{X^s}_{u(n-1)}})$ - $\frac{(1+\betas)}{s}E(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}}$ and E$(\frac{{X^{\tau+1}}_{u(m)}}{{X^s}_{u(n)}})$ = $\frac{1}{(r+1)\beta}$ [E$(\frac{{X^{\tau+1}}}_u(m)}{{X^s}_{u(n-1)}})$ - E$(\frac{{X^{\tau+1}}_u(m)}}{{X^s}_{u(n-1)}})$ - (r+1)E$(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}})$]

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.15-22
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the power distribution. Let {$X_n$, $n{\geq}1$} be a sequence of independent an identically distributed random variables with a common continuous distribution function(cdf) $F(x)$ and probability density function(pdf) $f(x)$. Let $Y_n=max\{X_1,X_2,{\cdots},X_n\}$ for $n{\geq}1$. We say $X_j$ is an upper record value of {$X_n$, $n{\geq}1$}, if $Y_j$ > $Y_{j-1}$, $j$ > 1. The indices at which the upper record values occur are given by the record times {$u(n)$}, $n{\geq}1$, where $u(n)=min\{j{\mid}j>u(n-1),X_j>X_{u(n-1)},n{\geq}2\}$ and $u(1)=1$. Suppose $X{\in}POW(0,1,{\theta})$ then $$E\left(\frac{X^r_{u(m)}}{X^{s+1}_{u(n)}}\right)=\frac{\theta}{s}E\left(\frac{X^r_{u(m)}}{X^s_{u(n-1)}}\right)+\frac{(s-\theta)}{s}E\left(\frac{X^r_{u(m)}}{X^s_{u(n)}\right)\;and\;E\left(\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}\right)=\frac{\theta}{n+1}\left[E\left(\frac{X^{r+1}_{u(m-1)}}{X^s_{u(n+1)}}\right)-E\left(\frac{X^{r+1}_{u(m)}}{X^s_{u(n-1)}}\right)+\frac{r+1}{\theta}E\left(\frac{X^r_{u(m)}}{X^s_{u(n)}}\right)\right]$$.

• Journal of Korean Society of Archives and Records Management
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• v.9 no.1
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• pp.221-248
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• 2009

All records have attribute of representing the object, so archives should develop digital record exhibition to facilitate attribute that representing the object. If building cultural properties are chose as the represented object, it should be followed by analysis of nature values and record contents and applied to the suitable framework. Therefore, this study suggests the organized process of designing the framework which develops digital representing contents based on records.