Raleigh Distribution Research Articles

A New Discrete Raleigh Distribution and its Application in Immunogold Assay Data

Recently, discretization of continuous distribution was enchanted by many researchers especially in the field of reliability engineering and life testing. This is because the existing models are unsuited for many practical situations. For discretizing continuous distributions, various methods are available in literature. Among them a newly developed method is the two-stage composite discretization method which includes three different methodologies. Using these methodologies, we propose some new discretized distributions obtained through the discretization of Rayleigh distribution. We compare the hazard rate functions of Rayleigh, Discrete Rayleigh with the newly proposed discrete distributions. The flexibility of the model is illustrated using immunogold assay data.

Technical analysis of wind energy potentials using a modified Weibull and Raleigh distribution model parameters approach in the Gambia

Wind energy has gained prominence over the past few decades because of its environment-friendly nature and abundant availability. However, the exploration of wind energy requires adequate knowledge of the wind distribution parameters before installing the wind turbine. This study assessed the potential of harvesting wind energy at two Gambian locations by fitting the best model comparing Weibull and Raleigh Distributions. A novel approach combining the energy pattern factor and standard deviation methods in estimating the distribution parameters of the characteristics of wind in the Gambian locations of Yundum and Basse has been presented and statistically analyzed using the Weibull and Raleigh distribution functions. The results showed that the shape parameters ranged from 4.88 to 6.98 and 3.87–6.15 for Yundum and Basse locations, the Weibull scale parameter ranged from 6.60 to 10.58 m/s and 4.51–8.69 m/s for Yundum and Basse while the calculated wind power densities ranged from 139 to 718 W/m2 and 46–390 W/m2 for Yundum and Basse respectively. These results clearly show a high potential for generating electricity with wind in the study areas. The statistical analysis revealed that the Weibull models perform better at Yundum in terms of RMSD = 0.33, NSCOE=0.45,MAE=0.29 and χ2= 1.57 while the Raleigh distribution gives a better fit for Basse in terms of R2=0.88, and MAE=0.39 only making it more suitable for calculating the wind power potentials.

An intermediate water gravity wavelength and wave height measurement inside a large wave flume tank

This paper discusses an intermediate water gravity wavelength and wave height measurement method. Three methods were used to obtain wave height, wavelength, and period. Firstly, conventional methods used two Honeywell pressure sensors mounted at the bottom of the wave tank at two different locations. Secondly, using the transfer function of the flap wavemaker (the relationship between wave height and the wave paddle stroke). Thirdly, the Laser Sheet technique (PIV image processing technique). The significant wave height and period from pressure reading sensors of regular gravity waves were obtained from the Raleigh distribution and Zero up crossing technique. Wavelength was obtained indirectly by using a dispersion relationship that was solved by using the Newton Raphson numerical method from both the pressure sensors and the transfer function of the flap wavemaker. This experiment was focused on getting the direct value of wave measurements by developing an image processing technique in a clear large wave flume tank to replace the conventional methods and eliminate the error that may produce by using the numerical methods. The PIV setup with the CCD camera was used to capture wave images. The image processing technique based on Canny edge detection with constant threshold value was used to detect the edge of the waves. The experimental result showed a good agreement between the results obtained from these three methods, with the percent of error up to 8.683%.

Estimation of the reliability function of the Rayleigh distribution using some robust and kernel methods

The research presents the reliability. It is defined as the probability of accomplishing any part of the system within a specified time and under the same circumstances. On the theoretical side, the reliability, the reliability function, and the cumulative function of failure are studied within the one-parameter Raleigh distribution. This research aims to discover many factors that are missed the reliability evaluation which causes constant interruptions of the machines in addition to the problems of data. The problem of the research is that there are many methods for estimating the reliability function but no one has suitable qualifications for most of these methods in the data such as the presence of anomalous values or extreme values or the appropriate distribution of these data is unknown. Therefore, the data need methods through which can be dealt with this problem. Two of the estimation methods have been used: the robust (estimator M) method and the nonparametric Kernel method. These estimation methods are derived to arrive at the formulas of their capabilities. A comparison of these estimations is made using the simulation method as it is implemented. Simulation experiments using different sample sizes and each experiment is repeated (1000) times to achieve the objective. The results are compared by using one of the most important statistical measures which is the mean of error squares (MSE). The best estimation method has been reached is the robust (M estimator) method. It has been shown that the estimation of the reliability function gradually decreases with time, and this is identical to the properties of this function.

Diagnoses in the Aging Process of Residential Buildings Constructed Using Traditional Technology

The perspective of maintaining residential buildings in adequate technical condition is one of the most important problems over the course of their service life. The aim of the work is to present issues connected with the methods of predicting the process of changes in performance characteristics over the entire period that a building, constructed using traditional technology, is operational. Identification of the technical situation consists of a prognosis based on the analytical form of the distribution function and probability density of building usability. The technical condition of a building results from its past, while familiarity with the condition is necessary to determine how the building will behave in the future. The presented predictive diagnostics of the performance characteristics of an entire building and its elements is an original methodology of describing the lifespan of a building. In addition to identifying the technical condition, its aim is also to aid in making decisions regarding maintenance works. The developed model of predicting changes in the performance characteristics of buildings, the Prediction of Reliability according to Exponentials Distribution (PRED), is based on the principles applied for technical devices. The model is characterized by significant limitations in its application due to the negligible influence of wear processes. In connection with the above, the Prediction of Reliability according to Raleigh Distribution (PRDD) was developed, where the carried-out processes of changes in the performance characteristics are described using Rayleigh’s distribution, and the building is a multi-element system. Model development would be incomplete without subjecting it to verification. Predicting the degree of the technical wear of load-bearing walls of a building is a form of checking the proposed PRED and PRRD models on the basis of data derived from periodical inspections of the research material. The developed model of the time distribution of the proper functioning of a building, presented as an image of the forecast of changes in the technical condition, can be applied to solving problems occurring in practice. The targeted approach to predicting the occurrence of damage will allow for optimal planning of maintenance works in buildings during their entire service life.

Assessment of Wind Power Potential Based on Raleigh Distribution Model: An Experimental Investigation for Coastal Zone

When compared with other renewable energy resources (RER), the wind energy share in the global energy production is increasing rapidly. Currently, the Government of Pakistan (GoP) is moving towards RER, specifically wind and solar energy. In this paper, the wind energy potential of Tando Ghulam Ali, Sindh, Pakistan is explored. For this purpose, one-year wind speed data is considered at various heights through various probability distribution functions (PDFs). Statistical comparison of Rayleigh, gamma, generalized extreme value (GEV) and lognormal PDFs have been done with two methods, namely root mean square error and (R^2) in order to select the best PDF. Results showed that the Rayleigh distribution function is the best at the above mentioned area for finding various factors like site selection and wind power cost per kWh.

Assessment of Wind Power Potential Based on Raleigh Distribution Model: An Experimental Investigation for Coastal Zone

Assessment of Wind Power Potential Based on Raleigh Distribution Model: An Experimental Investigation for Coastal Zone

Preventive Services of Residential Buildings According to the Pareto Principle

The problem of ensuring an adequate level of the technical condition of a building occurs over the entire period it is in service. In solving problems connected with developing a prediction of changes in performance characteristics of a residential building, it is suggested that algorithms of determining changes in the reliability of technical devices be used. The process of changes in the technical condition of technical equipment can be managed by making decisions regarding repairs or replacing components. The prognosis of unfavourable processes will make it possible to determine the time frame in which the technical condition of a building will be unsatisfactory in the future, and thus necessitate repair works. Applying optimal prophylactic replacements requires a knowledge of the time span that the components of the building can be expected to work properly. To model situations in survival analysis, the Rayleigh distribution for the random variable of time was accepted. In the article, the model of the life span curve for a residential building has been presented, where the Pareto principle was applied as the strategy for undertaking renovation works. Modelling various scenarios of use helps to choose the optimal planning of renovation works on a building. The characteristics of various strategies influence the shape of the life cycle curve of the building. Applying the Pareto principle is an example of a strategy of renovation works on residential buildings. Applying the Raleigh distribution to predict reliability is possible thanks to the analysis of a set of data including the values of the degrees of wear of actual residential buildings

Approximate Bayesian analysis of doubly censored samples from mixture of two Weibull distributions

The purpose of the paper is to estimate the parameters of the two-component mixture of Weibull distribution under doubly censored samples using Bayesian approach. The choice of Weibull distribution is made due to its (i) capability to model failure time data from engineering, medical and biological sciences (ii) added advantages over the well-known lifetime distributions such as exponential, Raleigh, lognormal and gamma distribution in terms of flexibility, increasing and decreasing hazard rate and closed-form distribution function and hazard rate. The proposed two-component mixture of Weibull distribution is even more flexible than its conventional form. However, the estimation of the parameters from the proposed mixture is more complex. Further, we have assumed couple of loss functions under non informative prior for the Bayesian analysis of the parameters from the mixture model. As the resultant Bayes estimators and associated posterior risks cannot be derived in the closed form, we have used the importance sampling and Lindley’s approximation to obtain the approximate estimates for the parameters of the mixture model. The comparison between the performances of approximation techniques has been made on the basis of simulation study and real-life data analysis. The importance sampling is found to be better than Lindley’s approximation as it gives better estimation for shape and mixing parameters of the mixture model and computations under this technique are much easier/shorter than those under Lindley’s approximation.

A generalized entropy optimization and Maxwell\u2013Boltzmann distribution

Based on the results of the diffusion entropy analysis of Super-Kamiokande solar neutrino data, a generalized entropy, introduced earlier by the first author is optimized under various conditions and it is shown that Maxwell–Boltzmann distribution, Raleigh distribution and other distributions can be obtained through such optimization procedures. Some properties of the entropy measure are examined and then Maxwell–Boltzmann and Raleigh densities are extended to multivariate cases. Connections to geometrical probability problems, isotropic random points, and spherically symmetric and elliptically contoured statistical distributions are pointed out.

Exponentiated Transmuted Generalized Raleigh Distribution: A New Four Parameter Rayleigh Distribution

This paper introduces a new four parameter Rayleigh distribution which generalizes the transmuted generalized Rayleigh distribution introduced by Merovci (2014). The new model is referred to as exponentiated transmuted generalized Rayleigh (ETGR) distribution. Various mathematical properties of the new model including ordinary and incomplete moments, quantile function, generating function and Renyi entropy are derived. We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. Two real data sets are used to compare the flexibility of the new model versus other models.

Multiple oscillations detection in control loops by using the DFT and Raleigh distribution

This work introduces an oscillation detection method by analyzing the magnitude of signal after the discrete Fourier transform (DFT). Properties of Raleigh distribution are used to calculate a threshold in order to detect multiple oscillations simultaneously. The proposed algorithm is able to detect oscillations in presence of colored noise based on a statistical test. Two simulation examples are provided to verify the effectiveness of the method.

Statistics-related and reliability-physics-related failure processes in electronics devices and products

The well known and widely used experimental reliability "passport" of a mass manufactured electronic or a photonic product — the bathtub curve — reflects the combined contribution of the statistics-related and reliability-physics (physics-of-failure)-related processes. When time progresses, the first process results in a decreasing failure rate, while the second process associated with the material aging and degradation leads to an increased failure rate. An attempt has been made in this analysis to assess the level of the reliability physics-related aging process from the available bathtub curve (diagram). It is assumed that the products of interest underwent the burn-in testing and therefore the obtained bathtub curve does not contain the infant mortality portion. It has been also assumed that the two random processes in question are statistically independent, and that the failure rate of the physical process can be obtained by deducting the theoretically assessed statistical failure rate from the bathtub curve ordinates. In the carried out numerical example, the Raleigh distribution for the statistical failure rate was used, for the sake of a relatively simple illustration. The developed methodology can be used in reliability physics evaluations, when there is a need to better understand the roles of the statistics-related and reliability-physics-related irreversible random processes in reliability evaluations. The future work should include investigations on how powerful and flexible methods and approaches of the statistical mechanics can be effectively employed, in addition to reliability physics techniques, to model the operational reliability of electronic and photonic products.

Study Position Distributing Rule on Dynamic Object

Aimed at the prime state problem about dynamic object position in the field, the statistical method is used to analyze distributing rule on dynamic object area position. Through studying the distributing theory on the dynamic object position, measuring the coordinate date of dynamic object and using statistical method such as hypotheses on normal distribution, hypotheses on exponential distribution, hypotheses on Raleigh distribution and hypotheses on the parameter, the distributing rule on dynamic object position is found. Based on the result of discussing each one test significance level, the distributing of dynamic object position can be is seen as hypotheses on exponential distribution in the level of significance.

Vertical characterization of the wind mode and its effect on the wind farm profitability of Sidi Daoud – Tunisia

The choice of a site and the statistical characterization of the wind speed represent the most significant factors in the process of wind park establishment. Indeed, the average value of the wind speed during one year and its temporal variation are the factors which have the greatest impact on the economic wind farm profitability. Thus, this article presents a meteorological and energetic study, in terms of the height of Sidi Daoud wind power station installed in Tunisia. From the meteorological data recorded, during the year 2004, in two places (masts 3 and 4) of the site and with heights 45, 50 and 60 m above ground level, we studied the vertical profile the wind speed both using the logarithmic law and the power law. The Raleigh distribution is selected to determine the annual characteristics of the wind and their influence on the available energy. The obtained results are then extrapolated vertically using the power law making it possible to make a comparative study between the two places in order to know the evolution of the wind speed at altitudes representing an energetic interest. The study also concerns the aerodynamic performances of the three aerogenerators with horizontal axis AE-46, AE-52 and AE-61 installed in site. From their characteristic curves, we have been able to study their energy efficiency in function of the wind speed, their use factors and the availability rate according to the height. All the numerical results illustrated in the article are obtained by a computer code developed by software MATLAB.

Network simulation for deep bed filtration of Brownian particles—a supplement

The track of individual particles moving through a filter bed is simulated by applying the Brownian dynamics simulation method and the modified square network model. The effect of the Raleigh-type size distribution of particles and pores on the permeability reduction of porous media is also investigated. We find that the pore size distribution of porous media has a more profound effect on the reducing of the permeability ratio than that of the particle size distribution especially at the initial period of filtration. Straining is the main mechanism to reduce the permeability at the initial period of injection for the case of Raleigh distribution of the pore size, and vice versa for the case of unique size value where the direct deposition mechanism becomes dominant.

Hydrodynamic characteristics of moored floating pipe breakwaters in random waves

The hydrodynamic performance characteristics of a floating pipe breakwater (FPBW) model (row of pipes separated by a distance equivalent to the pipe diameter) moored to the flume floor with slack moorings has been investigated in random waves through an experimental programme. The tests have been conducted on three models each with pipes of different diameter. The average reflection and transmission coefficients are evaluated from measurements and reported as a function of relative breakwater width. The motion responses, as well as the variations in the forces on the seaside and lee side mooring lines, are also presented. In addition, statistical analysis has been carried out to prove that the heave and surge motions, as well as the peak mooring forces, follow the Raleigh distribution. The details of the models, set-up, experimental procedure and analysis of results are presented and discussed.

Modelling the Integrated Output of Mechanical Wind Pumps

A method for predicting output of simple multi-bladed windmill mechanically coupled to a reciprocating pump is proposed. The present method adopts an integrated approach by considering the interaction between the rotor, pump and the wind regime to model the wind pump discharge. The wind velocity-power relationship of the rotor is assumed to be quadratic. The wind regime is characterized by the Raleigh distribution. Differences in the starting and running torque requirements of the pump are also considered in the model. Wind data from a few potential sites from the southern part of India were analyzed and the expected outputs at these sites were predicted using the proposed method. [S0199-6231(00)00603-1]

Contribution of Supposed Wave Condition on Long-term Distribution of Wave Induced Load

This study is the second report concerned with statistical analysis on long-term distribution of wave induced load. In the first report, authors examined which factor gives influence by load revel in the long -term distribution, such as significant wave height, average wave period of supposed wave condition and relative angle between ship course and wave direction. The long-term distribution was decomposed into every these factors and a contribution rate analysis method for these factors in each load revel was introduced. Based on the method, it was clarified that the maximum wave induced stress value in the vicinity of the probability of exceedance around 10-8 can be governed by the most sever short-term wave condition which has the largest value of short-term wave induced Raleigh distribution parameter.In this report, the shape of the long-term distribution of the wave induced load for evaluation of fatigue strength is studied. Based on S-N curves and Miner's rule, the relation between the fatigue damage and supposed wave condition to calculate the long-term distribution is examined. The contribution rate analysis method for fatigue damage from supposed wave condition, such as significant wave height, average wave period of supposed wave condition and relative angle between ship course and wave direction, is introduced. It is shown that the most sever short-term wave condition, defined by the former report, also plays the most important role in the fatigue damage. The simple estimation method for long-term distribution described by Weibull distribution from the statistical propaty of the most sever short-term wave condition is introduced. Several examples show the applicability of the estimation method and estimation errors of the maximum value with probability exceedance 10-8 are less than 5% and of the fatigue damage rates are within 1030% large value.

WAVE STATISTICS ALONG THE NORTHERN COAST OF EGYPT

As a forerunner of a comprehensive study of wave and energy climate of the Nile Delta coast covering a period of more than 50 years, wave measurements taken in 3 locations along the coast in the year 1972 were statistically analysed. Shortcut methods based on statistical approach were used to analyse the wave records enabling quicker analysis. Spectral analysis of the wave records indicates narrow spectral band similar to Raleigh distribution. The histograms and frequency distribution curves of significant wave heights, and the relationships between various statistical prarameters such as H , H,,,,,, H,,,, and H also max 1/10' 1/3 rms agree closely with Raleigh distribution curves and parameters enabling the use of Raleigh distribution function in subsequent studies. Finally since the wave characteristics and wave energy climates are most important in the analysis of coastline changes, they are drawn from the data obtained from the analysis.