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A Theory of Offshore Bidding
Published in John Douglass Klein, The Impact of Joint Ventures on Bidding for Offshore Oil, 2017
The theory of order statistics helps to explain the overbidding problem. The ith order statistic is by definition the ith largest observation in a random sample. The median of a distribution--the middle observation in a sample--is probably the best known order statistic. In bidding theory, the first order statistic (largest observation) is of particular interest. The literature on order statistics derives actual distributions of various order statistics.22
Graphical displays of data and descriptive statistics
Published in Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke, Statistics in Engineering, 2019
Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke
A box-plot consists of a box extending from the lower quartile to the upper quartile and lines from the ends of the box to the least value and greatest value, that are not classed as outliers, respectively. Outliers are plotted as individual points. Numerical: (see Table 3.17) The main measures of centrality are sample mean (average) and median (middle value of sorted data).The most commonly used measure of spread is the variance together with its square root, the standard deviation.Approximately 2/3 of a data set will be within one standard deviation of the mean.If a variable is restricted to non-negative values, then the CV is the ratio of the standard deviation to the mean.The order statistics are the data sorted into ascending order. The sample quantile corresponding to a proportion p is the p(n + 1)th smallest datum.The lower quartile is estimated by the 0.25(n + 1)th smallest datum in the sample, and an approximation to this estimate can be found as the value of the variable corresponding to a cumulative proportion of 0.25 on the cumulative frequency polygon. The upper quartile is similarly estimated as the 0.75(n + 1)th smallest datum in the sample.The inter-quartile range is the difference between the upper and lower quartiles. It is a measure of spread and the central half of the data lies between the quartiles.
Exact Likelihood Inference for an Exponential Parameter under a Multi-Sample Type-II Progressive Hybrid Censoring Model
Published in American Journal of Mathematical and Management Sciences, 2022
Marcel Jansen, Erhard Cramer, Julian Gorny
The joint density function of the first progressively Type-II censored order statistics with censoring plan reads with and Then, conditionally on D, the joint density functions of Type-II progressive hybrid censored order statistics are given by (see Cramer et al., 2016) with or denote the cumulative distribution function and density function of a progressively Type-II censored order statistic with censoring plan respectively, Note that the conditional joint density function given in (5) corresponds to the counter setting whereas the density functions given in Eqs. (6) and (7) correspond to the counter setting
Sign control chart based on ranked set sampling
Published in Quality Technology & Quantitative Management, 2018
Samaneh Asghari, Bahram Sadeghpour Gildeh, Jafar Ahmadi, Golamreza Mohtashami Borzadaran
where denotes rth order statistic from the rth row. These steps can be repeated m times (cycles) to produce a balanced RSS of size . If the ranks do tally with the numerical orders, the ranking is said to be perfect, otherwise, it is said to be imperfect. In this study, we only concentrated perfect ranking case. In the RSS scheme, each of the elements are independent and distributed as the order statistic. If denotes the probability density function (pdf) of the order statistic () from a random sample of size k with pdf and cumulative distribution function (cdf) , then from *arnold1992first, the pdf of is given by
Seasonality patterns in the container shipping freight rate market
Published in Maritime Policy & Management, 2018
This section presents the Monte Carlo finite sample with critical values for the specific case of CCFI. The asymptotic distribution of the five F-statistics, , are the same (Joseph and Miron 1993). Table 2 contains the critical values from the finite sample of the distributions of the F-statistics needed to employ the HEGY procedure with monthly data. The critical values were obtained by simulating the 5000 regressions of Equation (6) . The fundamental series were generated by , with standard normal . The critical values for the F-statistics were calculated by combing the observations for all five statistics. That is, F-statistics are computed by stacking and calculating the order statistic for the (25,000*1) vector. Thus, the F-statistics are based on 25,000 observations.