General Form Of Distribution Research Articles

Spherically symmetric de Sitter solution of black holes

In this study, we obtain the solution of the spherically symmetric de Sitter solution of black holes using a general form of distribution functions which include Gaussian, Rayleigh and Maxwell–Boltzmann distributions as a special case. We investigate the properties of thermodynamic variables such as the Hawking temperature, the entropy, the mass and the heat capacity of black holes. Moreover, we show that the strong energy condition which includes the null energy condition is satisfied. Finally, we show the regularity of the solution by calculating the scalar curvature and invariant curvature in general distribution form.

On Distribution of Sums of Random Variables with Invariant Links and their Modeling

A general form of distribution of a sum of a finite number of absolutely continuous random variables is obtained, examples of constructing and modeling sequences with averaged links (with invariant links) are considered based on the distribution of the sum of these random variables

Bi-Level Multi-Objective Stochastic Linear Fractional Programming with General form of Distribution

This paper deals with the stochastic approach of bi-level multi-objective linear fractional programming problem.In this type of bi-level programming problem stochastic nature the right hand side resource vector is considered to follow a general form of distribution F (bi) = 1 − Bi^exp(Aih(bi))[13], which in itself includes many well known distributions such as Pareto distribution, Weibull distribution etc. After converting the problem into an equivalent deterministic form, each level of the problem is transformed into a single objective by using K-T conditions. Finally the problem is solved by Taylors series approach. A numerical example is also presented to illustrate how the proposed approach is utilized.

Multiple Conversions of Measurements for Nonlinear Estimation

A multiple conversion approach (MCA) to nonlinear estimation is proposed in this paper. It jointly considers multiple hypotheses on the joint distribution of the quantity to be estimated and its measurement. The overall MCA estimate is a probabilistically weighted sum of the hypothesis conditional estimates. To describe the hypothesized joint distributions used to match the truth, a general distribution form characterized by a (linear or nonlinear) measurement conversion is found. This form is more general than Gaussian and includes Gaussian as a special case. Moreover, the minimum mean square error (MMSE) optimal estimate, given a hypothesized distribution in this form, is simply the linear MMSE (LMMSE) estimate using the converted measurement. LMMSE-based estimators, including the original LMMSE estimator and its generalization—the recently proposed uncorrelated conversion based filter—can all be incorporated into the MCA framework. Given a nonlinear problem, a specific form of the hypothesized distribution can be optimally obtained by quadratic programming using the information in the nonlinear measurement function and the measurement conversion. Then, the MCA estimate can be obtained easily. For dynamic problems, an interacting multiple conversion algorithm is proposed for recursive estimation. The MCA approach has a simple and flexible structure and takes advantage of multiple LMMSE-based nonlinear estimators. The overall estimates are obtained adaptively depending on the performance of the candidate estimators. Simulation results demonstrate the effectiveness of the proposed approach compared with other nonlinear filters.

A unified expression for grain size distribution of soils

Grain size distribution (GSD) is fundamental for soils and usually described by a set of graphic parameters (e.g., median size, kurtosis, skewness, uniform and curvature coefficient). Some probability distributions (e.g., lognormal and Weibull distribution) are used for special cases, but no general expression is available. In this paper we propose a general distribution form of P(D)=CD−μexp(−D/Dc) for various soil materials, with P(D) the exceedance percentage and C, μ and Dc are parameters determined by the grain size frequency data. The power-law and exponential part of this expression respectively responds to the self-similar and random processes of grain fragmentation and accumulation in soil generation and evolution. The GSD parameters are distinct in soils and their variation reflects the changes in grain composition, such as the grain migration and segregation in landslides, avalanches, debris flows and sedimentary deposits. In addition, the GSD also fits the pore size of granular materials, confirming the grain-pore duality and suggesting an important role of the GSD expression in dynamics of soils and granular media in general.

Multi-choice stochastic transportation problem involving general form of distributions.

Many authors have presented studies of multi-choice stochastic transportation problem (MCSTP) where availability and demand parameters follow a particular probability distribution (such as exponential, weibull, cauchy or extreme value). In this paper an MCSTP is considered where availability and demand parameters follow general form of distribution and a generalized equivalent deterministic model (GMCSTP) of MCSTP is obtained. It is also shown that all previous models obtained by different authors can be deduced with the help of GMCSTP. MCSTP with pareto, power function or burr-XII distributions are also considered and equivalent deterministic models are obtained. To illustrate the proposed model two numerical examples are presented and solved using LINGO 13.0 software package.

MOMENTS OF LOWER GENERALIZED ORDER STATISTICS FROM DOUBLY TRUNCATED CONTINUOUS DISTRIBUTIONS AND CHARACTERIZATIONS

In this paper, we derive recurrence relations for moments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, generalized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribution based on single moments of lower generalized order statistics are given.

A distribution-free method for forecasting non-gaussian time series

The non-linear instantaneous transformation is a method to model and forecast non-Gaussian time series. A restriction of this method is that the marginal distribution of data must be known, or a general distribution form has to be determined. A difficulty of this method is that in practice the distribution of observed data is usually unknown, and it needs to be determined by fitting the data. In this study, a distribution-free plotting position formula is applied to the non-linear instantaneous transformation method. Synthetic time series and observed data are used to illustrate the proposed method, which does not require fitting the marginal distribution of the data to be forecasted.

Separability of item and person parameters in response time models

This paper discusses two forms of separability of item and person parameters in the context of response time (RT) models. The first is “separate sufficiency”: the existence of sufficient statistics for the item (person) parameters that do not depend on the person (item) parameters. The second is “ranking independence”: the likelihood of the item (person) ranking with respect to RTs does not depend on the person (item) parameters. For each form a theorem stating sufficient conditions, is proved. The two forms of separability are shown to include several (special cases of) models from psychometric and biometric literature. Ranking independence imposes no restrictions on the general distribution form, but on its parametrization. An estimation procedure based upon ranks and pseudolikelihood theory is discussed, as well as the relation of ranking independence to the concept of double monotonicity.