Rayleigh distribution

... and small scale fading in indoor wireless communication channels. Reinaldo A. Valenzuela, Dmitry Chizhik and Jonathan Ling ... References [I] R. A. Valenzuela, 0. Landron, DL Jacobs, "Estimating Local Mean Signal Strength of Indoor Multipath Propagation", IEEE Trans. ...

Assumes the life distribution of a test unit for any stress follows a Rayleigh distribution with scale parameterθ, and that)(θLn is a linear function of the stress level. Maximum likelihood estimators of the parameters under a cumulative exposure model are obtained. The approximate variance estimates obtained from the asymptotic normal distribution of the maximum likelihood estimators are used to construct confidence intervals for the model parameters. A simulation study was conducted to study the performance of the estimators. Simulation results showed that in terms of bias, mean squared error, attainment of the nominal confidence level, symmetry of lower and upper error rates and the expected

In this present article, we have proposed a new probability distribution known as Exponentiated transmuted Rayleigh distribution and studied some statistical properties of the proposed model. Further, for application point of view, we have derived it from Rayleigh distribution as a baseline distribution and proved its application in comparison to the its sub-models in terms of fitting a real data as well as simulated data through Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC) and log likelihood (LL) criterion of goodness of fit.

Energy supply in Nigeria is a major problem for both large and small-scale purposes. The potential of wind power for generation and sustainable electricity supply is yet to be adequately harnessed. Therefore, this study empirically investigated wind characteristics and potentials over four meteorological stations (Calabar, Uyo, Warri, and Ikeja) within the coastal region of Nigeria using 4-year (2008-2011) wind speed data obtained from the archive of Nigerian Meteorological Agency (NiMET). The wind characteristics were evaluated using descriptive analysis. The Weibull and Rayleigh probability density function and cumulative distribution function were fitted with the actual observed wind frequencies at 10 m, and accuracy assessment of the goodness of fit was carried out using some selected error metrics. The Weibull shape factor (k) and scale parameter (c) were calculated and used to estimate Weibull wind speeds and wind power density at 10 m and hub height 70 m using power law. Results revealed that, the maximum mean monthly wind speeds of 3.88 m/s in December, 4.73 m/s in January, 3.98 m/s in April, and 8.37 m/s in August, were observed over Calabar, Uyo, Warri, and Ikeja respectively. The performance evaluation of the distribution fit revealed that RMSE (ranging from 0.01 to 0.06) and χ 2 (ranging from 0.001 to 0.23) are very low for Weibull and high RMSE (0.03-0.33) and χ 2 (0.003-13.91) for Rayleigh, while r (>0.9) and COE (>0.8) were both high over all the stations and for the periods of study. The study concludes that Weibull model could be adopted as the best over Rayleigh for representing wind speed distributions over the coastal region and also Ikeja area can be considered as very suitable for wind turbine applications thus, the wind power potential in this area should be adequately harnessed in order to increase the power supply and reduce carbon dioxide emissions.

The Rayleigh distribution was proposed in the fields of acoustics and optics by lord Rayleigh. It has wide applications in communication theory, such as description of instantaneous peak power of received radio signals, i.e. study of vibrations and waves. It has also been used for modeling of wave propagation, radiation, synthetic aperture radar images, and lifetime data in engineering and clinical studies. This work proposes two new extensions of the Rayleigh distribution, namely the Rayleigh inverted-Weibull (RIW) and the Rayleigh Weibull (RW) distributions. Several fundamental properties are derived in this study, these include reliability and hazard functions, moments, quantile function, random number generation, skewness, and kurtosis. The maximum likelihood estimators for the model parameters of the two proposed models are also derived along with the asymptotic confidence intervals. Two real data sets in communication systems and clinical trials are analyzed to illustrate the concept of the proposed extensions. The results demonstrated that the proposed extensions showed better fitting than other extensions and competing models.

The generalized Rayleigh (GR) distribution [V.G. Vodǎ, Inferential procedures on a generalized Rayleigh variate, I, Appl. Math. 21 (1976), pp. 395–412; V.G. Vodǎ, Inferential procedures on a generalized Rayleigh variate, II, Appl. Math. 21 (1976), pp. 413–419] has been applied in several areas such as health, agriculture, biology and other sciences. For the first time, we propose the Kumaraswamy GR (KwGR) distribution for analysing lifetime data. The new density function can be expressed as a mixture of GR density functions. Explicit formulae are derived for some of its statistical quantities. The density function of the order statistics can be expressed as a mixture of GR density functions. We also propose a linear log-KwGR regression model for analysing data with real support to extend some known regression models. The estimation of parameters is approached by maximum likelihood. The importance of the new models is illustrated in two real data sets.

ABSTRACT Life testing components, or products having a one-parameter Rayleigh distribution which age with time, are considered. Using the natural conjugate family of priors, we derive the posterior distribution, and hence the predictive distribution of the future observations. The Bayesian predictive interval is compared with classical counterparts. A numerical example is given.

In this study, the software development cost model of the Rayleigh-type (inverse Rayleigh and Rayleigh) lifetime distribution was compared with the Goel-Okumoto basic model, and the attributes of software development cost and optimal release time were newly analyzed. For this purpose, software failure time data were used, parameter estimation was applied to the maximum likelihood estimation method, and nonlinear equations were calculated using the bisection method. As a result, we confirmed that the Rayleigh model is efficient because it has lower software development costs and faster software release time than the inverse Rayleigh model. Also, it was confirmed that the Rayleigh model is the most efficient among the proposed model. Through this study, we newly analyzed the software development cost and release time of the inverse Rayleigh and Rayleigh distribution which has no previous study case. Also, it is expected that software developers will be able to use this study data as a basic guideline for exploring the property of economical software development cost and optimal release time.