Some characteristic parameters of Gaussian plume model

The Gaussian solution of the diffusion equation for line source is used to have the first four moments of the vertical concentration distribution (centroid, variance, skewness, and kurtosis). The magnitude and position of maximum concentration level were evaluated. Also the plume advection wind speed is estimated. Equations for the ground level concentration were compared with wind tunnel measurements.

Reliability Assessment on Pile Foundation Bearing Capacity Based on the First Four Moments in High-Order Moment Method

In this paper, the high-order moment method (HOMM) was developed for estimating pile foundation bearing capacity reliability assessment. Firstly, after the performance function was established, the first four moments (viz. mean, variance, skewness, and kurtosis) were suggested to be determined by a point estimate method based on two-dimensional reduction integrations. Then, the probability distribution of the performance function for the pile foundation bearing capacity was then approximated by a four-parameter cubic normal distribution, in which its distribution parameters are the first four moments. Meanwhile, the quantile of the probability distribution for the performance function and its reliability index was capable to be obtained through this distribution. In order to examine the efficiency of this method in engineering application, four pile foundations with different length-diameter radios were investigated in detail. The results demonstrate that the reliability analysis based on HOMM is greatly improved to the computational efficiency without loss precision compared with Monte Carlo simulation (MCS) and does not require complex partial derivative solving, checking point sought, and large numbers of iteration comparing with first-order reliability method (FORM). Moreover, the probability distribution function (PDF) approximated by the four-parameter cubic normal distribution was found to be consistent with that obtained by MCS. Eventually, the effects of parameter sensitivity for relative soil layer of the certain pile on reliability index were illustrated using the above-mentioned method. It indicated that the HOMM is an effective and simple approach for reliability assessment of the pile foundation bearing capacity.

Quantitative traits under selection: derivations of distributions, higher moments, and the effects of recombination

The mathematical theory of quantitative traits is over one hundred years old but it is still a fertile area for research and analysis. However, the effects of selection on a quantitative trait, while well understood for the effects on the mean and variance, have traditionally been difficult to attack from the perspective of analyzing the probability density of the breeding values and deriving higher (third and fourth) moments as well as analyzing the impact of recombination. In this paper, the exact formula for the breeding value distribution after selection is derived and, using new integral tables, the first four moments are given exact expressions for the first time. In addition, the effects of recombination on the full distribution of breeding values are demonstrated. Finally, the changes of GXE covariance in the selected parent population caused by factors similar to the Bulmer Effect are also investigated in detail.

Samade Probability Distribution: Its Properties and Application to Real Lifetime Data

A new two-parameter lifetime distribution has been proposed in this study. The distribution is called Samade distribution. The model is motivated by the wide use of the lifetime models derived from the mixture of gamma and exponential distributions. Its mathematical properties which include the first four moments, variance as well as coefficient of variation, reliability function, hazard function, survival function, Renyi entropy measure and distribution of order statistics have been successfully derived. The maximum likelihood estimation of its parameters and application to real life data have been discussed. Application of this model to three real datasets shown that the proposed model yields a satisfactorily better fit than other existing lifetime distributions. The comparism of goodness-of-fits were established using -2Loglikelihood, AIC and BIC.

Response Time Distribution in a Tandem Pair of Queues with Batch Processing

Response time density is obtained in a tandem pair of Markovian queues with both batch arrivals and batch departures. The method uses conditional forward and reversed node sojourn times and derives the Laplace transform of the response time probability density function in the case that batch sizes are finite. The result is derived by a generating function method that takes into account that the path is not overtake-free in the sense that the tagged task being tracked is affected by later arrivals at the second queue. A novel aspect of the method is that a vector of generating functions is solved for, rather than a single scalar-valued function, which requires investigation of the singularities of a certain matrix. A recurrence formula is derived to obtain arbitrary moments of response time by differentiation of the Laplace transform at the origin, and these can be computed rapidly by iteration. Numerical results for the first four moments of response time are displayed for some sample networks that have product-form solutions for their equilibrium queue length probabilities, along with the densities themselves by numerical inversion of the Laplace transform. Corresponding approximations are also obtained for (non-product-form) pairs of “raw” batch-queues—with no special arrivals—and validated against regenerative simulation, which indicates good accuracy. The methods are appropriate for modeling bursty internet and cloud traffic and a possible role in energy-saving is considered.

The Performance of Estimators for Generalization of Crack Distribution

In this research, we propose a new four parameter family of distributions called Generalized Crack distribution. We generalizes the family three parameter Crack distribution. The Generalized Crack distribution is a mixture of two parameter Inverse Gaussian distribution, Length-Biased Inverse Gaussian distribution, Twice Length-Biased Inverse Gaussian distribution, and adding one more weight parameter . It is a special case for , where and is the weighted parameter. We investigate the properties of Generalized Crack distribution including first four moments, parameters estimation by using the maximum likelihood estimators and method of moment estimation. Evaluate the performance of the estimators by using bias. The results of simulation are presented in numerically and graphically.

A Global-Scale Investigation of Stochastic Similarities in Marginal Distribution and Dependence Structure of Key Hydrological-Cycle Processes

To seek stochastic analogies in key processes related to the hydrological cycle, an extended collection of several billions of records from hundred thousands of worldwide stations is used in this work. The examined processes are the near-surface hourly temperature, dew point, relative humidity, sea level pressure, and atmospheric wind speed, as well as the hourly/daily streamflow and precipitation. Through the use of robust stochastic metrics such as the K-moments and a second-order climacogram (i.e., variance of the averaged process vs. scale), it is found that several stochastic similarities exist in both the marginal structure, in terms of the first four moments, and in the second-order dependence structure. Stochastic similarities are also detected among the examined processes, forming a specific hierarchy among their marginal and dependence structures, similar to the one in the hydrological cycle. Finally, similarities are also traced to the isotropic and nearly Gaussian turbulence, as analyzed through extensive lab recordings of grid turbulence and of turbulent buoyant jet along the axis, which resembles the turbulent shear and buoyant regime that dominates and drives the hydrological-cycle processes in the boundary layer. The results are found to be consistent with other studies in literature such as solar radiation, ocean waves, and evaporation, and they can be also justified by the principle of maximum entropy. Therefore, they allow for the development of a universal stochastic view of the hydrological-cycle under the Hurst–Kolmogorov dynamics, with marginal structures extending from nearly Gaussian to Pareto-type tail behavior, and with dependence structures exhibiting roughness (fractal) behavior at small scales, long-term persistence at large scales, and a transient behavior at intermediate scales.

On a Generalised Exponential-Lindley Mixture of Generalised Poisson Distribution

Background: A mixture distribution arises when some or all parameters in a mixing distribution vary according to the nature of original distribution. A generalised exponential-Lindley distribution (GELD) was obtained by Mishra and Sah (2015). In this paper, generalized exponential- Lindley mixture of generalised Poisson distribution (GELMGPD) has been obtained by mixing generalised Poisson distribution (GPD) of Consul and Jain’s (1973) with GELD. In the proposed distribution, GELD is the original distribution and GPD is a mixing distribution. Generalised exponential- Lindley mixture of Poisson distribution (GELMPD) was obtained by Sah and Mishra (2019). It is a particular case of GELMGPD. Materials and Methods: GELMGPD is a compound distribution obtained by using the theoretical concept of some continuous mixtures of generalised Poisson distribution of Consul and Jain (1973). In this mixing process, GELD plays a role of original distribution and GPD is considered as mixing distribution. Results: Probability mass of function (pmf) and the first four moments about origin of the generalised exponential-Lindley mixture of generalised Poisson distribution have been obtained. The method of moments has been discussed to estimate parameters of the GELMGPD. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature. P-value of this distribution has been compared to the PLD of Sankaran (1970) and GELMPD of Sah and Mishra (2019) for similar type of data-sets. Conclusion: It is found that P-value of GELMGPD is greater than that in each case of PLD and GELMPD. Hence, it is expected to be a better alternative to the PLD of Sankaran and GELMPD of Sah and Mishra for similar types of discrete data-sets which are negative binomial in nature. It is also observed that GELMGPD gives much more significant result when the value of is negative.

Reliability Analysis of Mechanical Systems Based on the First Four Moments of Input Parameters

The performance of a mechanical or structural system can be improved through a proper selection of its design parameters such as the geometric dimensions, external actions (loads) and material characteristics. The computation of the reliability of a system, in general, requires a knowledge of the probability distributions of the parameters of the system. It is known that for most practical systems, the exact probability distributions of the parameters are not known. However, the first few moments of the parameters of the system may be readily available in many cases from experimental data. The determination of the reliability and the sensitivity of reliability to variations or fluctuations in the parameters of the system starts with the establishment of a suitable limit state equation. This work presents a reliability analysis approach for mechanical and structural systems using the fourth order moment function for approximating the first four moments of the limit state function. By combining the fourth-order moment function with the probabilistic perturbation method, numerical methods are developed for finding the reliability and sensitivity of reliability of the system. An automobile brake and a power screw are considered for demonstrating the methodology and effectiveness of the proposed computational approach. The results of the automobile brake are compared with those given by the Monte Carlo method.

Soliton turbulence in electronegative plasma due to head-on collision of multi solitons

Head-on interaction of four dust ion acoustic (DIA) solitons and the statistical properties of the wave field due to head-on interaction of solitons moving in opposite direction is studied in the framework of two Korteweg de Vries (KdV) equations. The extended Poincaré–Lighthill–Kuo (PLK) method is applied to obtain two opposite moving KdV equations from an unmagnetized four component plasma model consisting of Maxwellian negative ions, cold mobile positive ions, κ-distributed electrons and positively charged dust grains. Hirota’s bilinear method is adopted to obtain two-soliton solutions of both the KdV equations and accordingly act of soliton turbulence is presented due to head-on collision of four solitons. The amplitude and shape of the resultant wave profile at the point of strongest interaction are obtained. To see the effect of head-on collision on the statistical properties of wave field the first four moments are computed. It is observed that the head-on collision has no effect on the first integral moment while the second, third and fourth moments increase in the dominant interaction region of four solitons, which is a clean indication of soliton turbulence.