K-distribution

About: K-distribution is a research topic. Over the lifetime, 1281 publications have been published within this topic receiving 51774 citations.

Verification of Accuracy in Statistical Estimations for Probability Distributions Having Tails of Special Shape

Abstract: Statistical estimations for probability distributions having tails of special shape, such as a double-mode distri-bution as well as the so-called heavy-tailed or fat-tailed distribution, are quantitatively discussed through virtual experiments using computer simulations. In this paper, a probability distribution describing the damage degree of concrete liners of tunnels in cold region is examined as an example of the double-mode probability distribution. First, virtual data sets of observations are generated by the use of quasi-random numbers for a Pareto distribution as a typical example of the fat-tailed distribution, whereas the actual data set obtained for the damage degree of concrete liners is used for generating virtual data set for the double-mode distribution. Next, statistical estimations are executed by the use of probability papers to identify the probability distribution showing the “best” fitting among supposed plural candidates for probability distributions. Finally, the accuracy of the estimation is quantified by applying the coefficient of determination. The results show that the accuracy of the estimation in the tail region is scarcely improved even if the number of data is increased.

Application of extreme value theory to the bec family of distributions

Abstract: Arnold and Strauss (1988) derived a family of bivariate life distributions having the property that the conditional distributions are exponential. Asymptotic distributions for the marginal and bivariate extremes for this family of distributions are derived employing the asymptotic theory of extreme order statistics.

The extended generalized gamma distribution which is useful for hydrological statistics and its parameter estimation method

Abstract: In hydrologic frequency analysis, a variety of probability distribution functions, such as the gamma, log-normal, extreme-value, and log-gamma, are often examined whether they are appropriate to the flood data or not by using some hypothesis testing methods, because the properties of the flood data are not well understood even now. In order to find a property of the flood data, we can use another method: using the more general probability distribution function which includes many types of probability distributions used for hydrological statistics. The 4-parameter extended generalized gamma distribution function is one of such distribution functions. Two types of the extended distributions are proposed. The parameter estimation method is also introduced.

An Algorithm for Lead Time Demand Distributions

Abstract: This paper presents a recursive algorithm to compute the lead time aggregate demand distribution from the arrival distributions of each order size. This algorithm can compute the aggregate demand distribution directly from numerical data of arrival frequencies without first fitting the data frequencies to standard distributions. When the arrival distributions do follow certain standard distributions, the aggregate demand distribution can be computed explicitly. The cases of Poisson distributions and negative binomial distributions are demonstrated as examples.