• Journal of the Korean Statistical Society
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• v.35 no.2
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• pp.167-177
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• 2006

An important role of statistical analysis in science is interpreting observed data as evidence, that is 'what do the data say?'. Although standard statistical methods (hypothesis testing, estimation, confidence intervals) are routinely used for this purpose, the theory behind those methods contains no defined concept of evidence and no answer to the basic question 'when is it correct to say that a given body of data represent evidence supporting one statistical hypothesis against another?' (Royall, 1997). In this article, we use likelihood ratios to measure evidence provided by record values in favor of a hypothesis and against an alternative. This hypothesis is concerned on mean of an exponential model and prediction of future record values.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.611-622
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• 2014

The inverse Weibull distribution (IWD) is the complementary Weibull distribution and plays an important role in many application areas. In Bayesian analysis, Soland's method can be considered to avoid computational complexities. One limitation of this approach is that parameters of interest are restricted to a finite number of values. This paper introduce nonparametric Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution (EIWD). In stead of Soland's conjugate piror, stick-breaking prior is considered and the corresponding Bayesian estimators under the squared error loss function (quadratic loss) and LINEX loss function are obtained and compared with other estimators. The results may be of interest especially when only record values are stored.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.441-446
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• 2003

Let { $X_{n}$ , n $\geq$ 1} be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function f(x). Let $Y_{n}$ = max{ $X_1$, $X_2$, …, $X_{n}$ } 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｜j>u(n-1), $X_{j}$ > $X_{u}$ (n-1), n$\geq$2} and u(1) = 1. We call the random variable X $\in$ Beta (1, c) if the corresponding probability cumulative function F(x) of x is of the form F(x) = 1-(1-x)$^{c}$ , c>0, 0$\leq$x$\leq$1. In this paper, we will give a characterization of the beta distribution of the first kind by considering conditional expectations of record values.s.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.463-469
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the exponential distribution. Let $\{X_n,\;n{\geq}1\}$ be a sequence of independent and identically distributed random variables with a common continuous distribution function 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 $X{\in}Exp(1)$. Then $\Large{E\;\left.{\frac{X^r_{u(m)}}{X^{s+1}_{u(n)}}}\right)=\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n)}}}\right)}$ and $\Large{E\;\left.{\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}}\right)=\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m-1)}}{X^s_{u(n-1)}}}\right)}$.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.497-503
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• 2005

This paper presents characterizations on the independence of the exponential and Pareto distributions by record values. Let ${X_{n},\;n {\ge1}$ be a sequence of independent and identically distributed(i.i.d) random variables with a continuous cumulative distribution function(cdf) F(x) and probability density function(pdf) f(x). $Let{\;}Y_{n} = max{X_1, X_2, \ldots, X_n}$ for n \ge 1. We say $X_{j}$ is an upper record value of ${X_{n},{\;}n\ge 1}, if Y_{j} > Y_{j-1}, j > 1$. The indices at which the upper record values occur are given by the record times {u(n)}, n \ge 1, where u(n) = $min{j|j > u(n-1), X_{j} > X_{u(n-1)}, n \ge 2}$ and u(l) = 1. Then F(x) = $1 - e^{-\frac{x}{a}}$, x > 0, ${\sigma} > 0$ if and only if $\frac {X_u(_n)}{X_u(_{n+1})} and X_u(_{n+1}), n \ge 1$, are independent. Also F(x) = $1 - x^{-\theta}, x > 1, {\theta} > 0$ if and only if $\frac {X_u(_{n+1})}{X_u(_n)}{\;}and{\;} X_{u(n)},{\;} n {\ge} 1$, are independent.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.501-505
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• 2012

In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.651-657
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• 2017

A sequence {$X_n,\;n{\geq}1$} of independent and identically distributed random variables with absolutely continuous (with respect to Lebesque measure) cumulative distribution function F(x) is considered. We obtain two characterizations of a family of continuous probability distribution by independence property of record values.

• The Journal of Advanced Prosthodontics
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• v.4 no.3
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• pp.153-157
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• 2012

PURPOSE. The study was conducted to compare the radiographic and clinical methods of measuring the horizontal condylar guidance (HCG) values. MATERIALS AND METHODS. The condylar guidance was measured using the radiographic (CT scan) and three clinical methods i.e. the wax protrusive records, Lucia jig record and intraoral central bearing device in 12 patients aged between 20-40 years irrespective of sex. The records were taken and transferred on the semi-adjustable articulator to record the HCG values. The CT scan was taken for 3D reconstruction of the mid facial region. Frankfort horizontal plane (FHP) and a line extending from the superior anterior most point on the glenoid fossa to the most convex point on the apex of articular eminence (AE) was marked on the CT scan. An angle between these two lines was measured on both right and left sides to obtain condylar inclination angle. Three interocclusal protrusive wax and jig records were taken and transferred to the semi adjustable articulator. Three readings were recorded on each side. Similarly the records were taken and transferred to the same articulator using the intra oral central bearing device to record the readings. RESULTS. The statistical analysis showed insignificant differences in the HCG values between the right and left sides [(P=.589 (CT), P=.928 (wax), P=.625 (jig), P=.886 (tracer)]. The clinical methods provided low Pearsons correlation values [(R = 0.423 (wax), R = 0.354 (jig), R = 0.265 (tracer)] for the right as well as the left sides when compared with the CT values. Among the clinical methods, jig and wax method showed strong level of association which is statistically significant while the intra-oral tracer showed weak association with the other two methods. CONCLUSION. The right and left HCG values were almost similar. The CT scan showed higher HCG values than the clinical methods and among the clinical methods, values obtained from all the methods were comparable.

• Journal of Nutrition and Health
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• v.34 no.6
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• pp.688-700
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• 2001

Nutrient intakes estimated using a 24-hr recall, a dirt record and a food frequency questionnaire(FFQ) were compared in a group of ninety-four elderly people(21 males, 73 females) in Cheongju, a city in Chung-Buk province. Mean intakes for energy, protein, Ca, p, Na, K thiamin and niacin obtained from the diet record were higher than those from the 24-hr recall. Mean intakes for energy, protein, Ca, P, Na, K thiamin, niacin and vitamin C from the FFQ were higher than those obtained from the 24-hr recall or the diet record. Correlation coefficients between the nutrient intake values from the 24-hr recall and those from the diet record ranged from 0.84 to 0.95 and were significantly correlated(p < 0.001). About 80% of the subjects in the lowest quintile by the 24-hr recall were also in the lowest two quintiles by the diet record. While the percentage fallen into the opposite category ranged from 0% to 15%. For most nutrients, at least 65% of the subjects when classified by the 24-hr recall fell into the same quintile when classified by the diet record, and the mean kappa value was 0.7. About 52% of the subjects in the lowest category by the 24-hr recall fell into the lowest two categories by FFQ. The mean percentage of the subjects in the lowest quintile by the diet record or in the lowest two quintiles by the FFQ was 51%. For most nutrients, at least 24% of each of the subjects when classified by both the 24-hr recall and the diet record fell into the same category when classified by the FFQ. The kappa values between the 24-hr recall or the diet recall and the FFQ were 0.17. These data indicate that in elderly subjects the 24-hr recall can provide very similar information to that obtained from the diet record but the FFQ can not provide good information if the right FFQ method is not used for only elderly subjects.

• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.479-493
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• 2012

The inverse Weibull distribution(IWD) is a complementary Weibull distribution and plays an important role in many application areas. In this paper, we develop a Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution(EIWD). We obtained Bayesian estimators through the squared error loss function (quadratic loss) and LINEX loss function. This is done with respect to the conjugate priors for shape and scale parameters. The results may be of interest especially when only record values are stored.