Parameter Estimations of Rayleigh Distribution

设随机变量X服从Rayleigh分布，其密度函数为p(x;β)=2x/βe-x^2/β，x＞0,β＞0为参数，对变换群G={gc;gc(x)=c^2x,c＞0}，本文分别在平方损失和熵损失下研究了β在G上的最优同变估计；当β有先验信息时，给出了β的Bayes估计。

A New Rayleigh Distribution:Properties and Estimation Based on Progressive Type-II Censored Data with an Application

In this paper,we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution.The new distribution contains one scale and one shape parameter and its hazard rate function can be increasing and bathtub-shaped.Some mathematical properties of the new distribution are derived including quantiles and moments.The parameters of modified Kies Rayleigh distribution are estimated based on progressively Type-II censored data.For this purpose,we consider two estimation methods,namely maximum likelihood and maximum product of spacing estimation methods.To compare the efficiency of the proposed estimators,a simulation study is carried out.To show the applicability of the new model as well as the estimation methods,one real data for failure times of software is analyzed.Based on the empirical parts,we can conclude that the proposed model can be considered as a good model in the field of life testing and reliability analysis compared with other competing models.

Statistical Inference for the Parameter of Rayleigh Distribution Based on Progressively Type-I Interval Censored Sample

In this paper, the estimation of parameters based on a progressively type-I interval censored sample from a Rayleigh distribution is studied. Different methods of estimation are discussed. They include mid-point approximation estima- tor, the maximum likelihood estimator, moment estimator, Bayes estimator, sampling adjustment moment estimator, sampling adjustment maximum likelihood estimator and estimator based on percentile. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their biases.

VOICE ACTIVITY DETECTION UNDER RAYLEIGH DISTRIBUTION

This paper presents an improved Voice Activity Detection （VAD） algorithm which uses the Signal-to-Noise Ratio （SNR） measure. We assume that noise Power Spectral Density （PSD） in each spectral bin follows a Rayleigh distribution. Rayleigh distributions with its asymmetric tail characteristics give a better description of the noise PSD distribution than Gaussian distribution. Under this asstlmption, a new threshold updating expression is derived. Since the analytical integral of the false alarm probability, the threshold updating expression can be represented without the inverse complementary error function and low computational complexity is achieved in our system. Experimental results show that the proposed VAD outperforms or at least is comparable with the VAD scheme presented by Davis under several noise environments and has a lower computational complexity.

Statistical Inference of Sine Inverse Rayleigh Distribution

We study in this manuscript a new one-parameter model called sine inverse Rayleigh(SIR)model that is a new extension of the classical inverse Rayleigh model.The sine inverse Rayleigh model is aiming to provide morefit-ting for real data sets of purposes.The proposed extension is moreflexible than the original inverse Rayleigh(IR)model and it hasmany applications in physics and medicine.The sine inverse Rayleigh distribution can havea uni-model and right skewed probability density function(PDF).The hazard rate function(HRF)of sine inverse Rayleigh distribution can be increasing and J-shaped.Sev-eral of thenew model’s fundamental characteristics,namely quantile function,moments,incompletemoments,Lorenz and Bonferroni Curves are studied.Four classical estimation methods forthe population parameters,namely least squares(LS),weighted least squares(WLS),maximum likelihood(ML),and percentile(PC)methods are discussed,and the performanceof the four estimators(namely LS,WLS,ML and PC estimators)are also compared bynumerical implementa-tions.Finally,three sets of real data are utilized to compare the behavior of the four employed methods forfinding an optimal estimation of the new distribution.

Statistical Inference of Truncated Weibull-Rayleigh Distribution: Its Properties and Applications

In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, such as reliability function, hazard function, reversed hazard rate function, cumulative hazard rate function, quantile function, rth moment, incomplete moments, Rényi and q entropies and order statistic. Parameter estimation is implemented using method of maximum-likelihood estimation and Fisher information matrix is derived. Finally, application of the presented new distribution to a real data representing the failure times of 63 airbcraft Windshield is given and its goodness-of-fit is demonstrated. In addition to, comparisons to other models are implemented to show the flexibility of the presented model.

Evaluating the lifetime performance index with the inverted exponentiated Rayleigh distribution based on censored sample

Lifetime performance index is a powerful and effective way to analyze whether a product achieves the specified standards.In this paper,we investigate the lifetime performance index for the inverted exponential Rayleigh distribution using progressive type II censored sample data.The censored sample is able to greatly save the cost of the experiment and speed up the experiment.We derive the estimation value of lifetime performance index using the maximum likelihood method,and conduct the hypothesis test.Based on extensive numerical simulation,the power function is utilized to assess effectiveness of hypothesis testing.The simulation results show that lifetime performance index is good for determining whether the lifetime of the product reaches the criterion.Finally,a practical dataset is provided to give a demonstration for the procedures of lifetime performance evaluation.

A Study on Mixture of Exponentiated Rayleigh and Exponentiated Exponential Distributions Based on Order Statistics

Mixtures of lifetime distributions occur when two different causes of failure arc present, each with the same parametric form of lifetime distributions. This paper is considered with the mixture model of exponentiated Rayleigh and exponentiated exponential distributions. The author＇s objectives are finding the statistical properties of the model and estimating the parameters of the model by using point estimation and interval estimation methods. First, some properties of the model with some graphs of the density function are discussed. Next, the maximum likelihood method of estimation is used for estimating scale and shape parameters of the model. Estimating the parameters is studied under complete and type II censored samples for different sample sizes. Asymptotic Fisher information matrix of the estimators for complete samples is founded with different sample sizes. The asymptotic variances of the maximum likelihood estimates are derived. Based on the asymptotic variances of the maximum likelihood estimates, interval estimates of the parameters are obtained. Some of the equations in this paper are solved by using numerical iteration such as Newton Raphson method by using Mathematica 7.0. The performance of findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation study based on absolute relative bias and mean square error.

Application of Maximum Entropy Principle to Studying the Distribution of Wave Heights in A Random Wave Field

Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.

A statistical inference for generalized Rayleigh model under Type-Ⅱ progressive censoring with binomial removals

This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.

Maximum entropy principle and statistical distribution of ocean wave heights

This paper concerns an application of a popular existing law, the maximum entropy principle, to the study of statistical distribution of the ocean wave heights. Under two proper premisses. a conclusion that the wave heights obey the Weibull distribution is drawn by making use of the maximum entropy principle. From this result, we hold that the intnnsic departures using the Rayleigh distribution to describe The realistic wave height must exist, and the Weibull distribution usually used as an empirical one has profound origin in physics. The Gluhovskli's empirical wave heights distribution relying on water depth is also discussed briefly, and a possible physical explanation associated with the maximum entropy principle is carried out.

A Statistical Analysis of Wind Speed and Power Density Based on Weibull and Rayleigh Models of Jumla, Nepal

In the present study, wind speed data of Jumla, Nepal have been statistically analyzed. For this purpose, the daily averaged wind speed data for 10 year period (2004-2014: 2012 excluded) provided by Department of Hydrology and Meteorology (DHM) was analyzed to estimate wind power density. Wind speed as high as 18 m/s was recorded at height of 10 m. Annual mean wind speed was ascertained to be decreasing from 7.35 m/s in 2004 to 5.13 m/s in 2014 as a consequence of Global Climate Change. This is a subject of concern looking at government’s plan to harness wind energy. Monthly wind speed plot shows that the fastest wind speed is generally in month of June (Monsoon Season) and slowest in December/January (Winter Season). Results presented Weibull distribution to fit measured probability distribution better than the Rayleigh distribution for whole years in High altitude region of Nepal. Average value of wind power density based on mean and root mean cube seed approaches were 131.31 W/m2/year and 184.93 W/m2/year respectively indicating that Jumla stands in class III. Weibull distribution shows a good approximation for estimation of power density with maximum error of 3.68% when root mean cube speed is taken as reference.

Analysis and Assessment of Wind Energy Potential of Almukalla in Yemen

Energy is an essential element for any civilized country’s social and economic development,but the use of fossil fuels and nonrenewable energy forms has many negative impacts on the environment and the ecosystem.The Republic of Yemen has very good potential to use renewable energy.Unfortunately,we find few studies on renewable wind energy in Yemen.Given the lack of a similar analysis for the coastal city,this research newly investigates wind energy’s potential near the Almukalla area by analyzing wind characteristics.Thus,evaluation,model identification,determination of available energy density,computing the capacity factors for several wind turbines and calculation of wind energy were extracted at three heights of 15,30,and 50meters.Average wind speeds were obtained only for the currently available data of five recent years,2005–2009.This study involves a preliminary assessment of Almukalla’s wind energy potential to provide a primary base and useful insights for wind engineers and experts.This research aims to provide useful assessment of the potential of wind energy in Almukalla for developing wind energy and an efficient wind approach.The Weibull distribution shows a perfect approximation for estimating the intensity of Yemen’s wind energy.Depending on both theWeibullmodel and the results of the annual wind speed data analysis for the study site in Mukalla,the capacity factor for many turbines was also calculated,and the best suitable turbine was selected.According to the International Wind Energy Rating criteria,Almukalla falls under Category 7,which is,rated“Superb”most of the year.

REAL TIME RECONSTRUCTION OF FLUID IN VIDEO

This paper puts forward a new method of realtime reconstruction of fluid in natural scene.It takes the measure of combination of image analysis and LBM(Lattice Boltz-mann Methods).First,employs LK(Lucas–Kanade)method to calculate the dense optical flow,and then takes LBM to obtain the joint force of central particles for the initial result.After backfilling the velocity vectors field,it adopts the K-means cluster to obtain several classes,in each class,it takes advantage of the Rayleigh distribution to fit the height field of fluid.Finally,the reconstruction result of fluid is obtained.In addition,it demonstrates the results of the height field of fluid in the experiment.Fur-ther experiments shows that it is a valid method of fluid reconstruction with real time and can be used in the study of natural landscape fluid with efficiency and feasibility.