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An extension of Rayleigh distribution and applications Kahkashan Ateeq 1*, Tahira Bano Qasim1 and Ayesha Rehman Alvi Abstract: In this article, we have derived a new distribution named as Rayleigh– Rayleigh distribution (RRD) motivated by the transformed transformer technique by Alzaatreh, Lee, and Famoye (2013). P. Nanthaprut et al. , The beta generalized Rayleigh distribution with applications to lifetime data. , 1. Our instrumentation products include analogue and digital square din switchboard instruments. ©2019 Tomy, et al . E. Gómez‐Déniz. Nichols MD, WJ Padgett. Corresponding Author. When k=1 the distribution is an Exponential Distribution and when k=2 the distribution is a Rayleigh Distribution . Y Y Box: 338, Tanzania. The cumulative distribution function is[2], for z Department of Statistics, St.Thomas College, India. Rayleigh distribution called the Weibull-Rayleigh distribution. ∈ {\displaystyle X} This distribution is well known and has been used for change-detection algorithms in low-frequency UWB SAR with good results. [8], The Rayleigh distribution was also employed in the field of nutrition for linking dietary nutrient levels and human and animal responses. 1Department of Statistics, Deva Matha College, India2Department of Statistics, St.Thomas College, India, Correspondence: Lishamol Tomy, Department of Statistics, Deva Matha College, Kuravilangad, Kerala-686633, India, Received: May 31, 2019 | Published: July 8, 2019, Citation: Tomy L, Gillariose J. {\displaystyle \sigma ,} In this research paper, a new class of life-time distribution is introduced by compounding A new generalization of Rayleigh distribution; properties and applications and The Exponentiated G Poisson model, the so-called Exponentiated Rayleigh Poisson distribution. The results are obtained from generating 1000 samples from the GR-TNB distribution. The Rayleigh distribution is a special case of the distribution with degrees of freedom parameter = 2 and scale parameter . Assuming that each component is uncorrelated, normally distributed with equal variance, and zero mean, then the overall wind speed (vector magnitude) will be characterized by a Rayleigh distribution. U Regret for the inconvenience: we are taking measures to prevent fraudulent form submissions by extractors and page crawlers. [9], Learn how and when to remove this template message. A new lifetime model: The Kumaraswamy generalized Rayleigh distribution. A generalized Rayleigh distribution and its application. {\displaystyle X} Cordeiro et al.,5 derived four-parameter beta-GR distribution, Gomes et al.,6 proposed the four-parameter Kumaraswamy-GR distribution, and MirMostafaee et al.,7 introduced Marshall-Olkin extended GR distribution respectively. This type of channel has an impulse response given by a delta which weighted has a power distribution function of Rayleigh: Where σ is the RMS of the received signal. Faton Merovci [5], generalizes the Rayleigh distribution using the quadratic rank transmutation map which was introduced by Shaw et al. The Exponentiated Kumaraswamy Distribution and Its Log-Transform. Abstract. A Rayleigh distribution is often observed when the overall magnitude of a vector is related to its directional components. Academic Editor: Alessandro De Gregorio. Topp-leone Rayleigh Distribution 3. One application for the Weibull or Rayleigh distribution are used to represent a probabilistic based model to estimate the wind power in a given region. This is obtained by applying the inverse transform sampling-method. The probability of 4.88 is 6.743-04% per the Rayleigh distribution, equation (10). An important characteristic of the Rayleigh distribution is that its hazard rate is a linearly increasing function of time at constant rate which makes it a suitable model for the lifetime of components/items that age rapidly with time. [3]. Rayleigh [16] derived it from the amplitude of sound resulting from many important sources. The pdf of survival function given in equation (4) is. The concluding remarks are given in Section 4. (1). For each replication, a random sample of size n = 50, 100 and 200 is drawn from the GR-TNB distribution. where Γa,x∫0xta−1e−tdt is the incomplete gamma function, hence statistical software"s can be used for various values of and . 2. In this section, we are focused on generalized Rayleigh truncated negative binomial (GR-TNB) distribution introduced by Jiju & Lishamol.1 The distribution is derived by using generator approach of Nadarajah et al.,8 They have examined various statistical properties of this distribution including estimation of parameters and have showed that this distribution is more flexible comparing to other generalizations of the rayleigh distribution. MG Babu. The Rayleigh distribution is a special case of the Weibull distribution.If A and B are the parameters of the Weibull distribution, then the Rayleigh distribution with parameter b is equivalent to the Weibull distribution with parameters A = 2 b and B = 2.. In the last two decades, generalization approaches were adopted and practiced by many statisticians. Cordeiro GM, Ortega EMM, Silva G. The Beta Extended Weibull Family. The Rayleigh distribution has wide range of applications in the field of applied sciences, especially in modeling the lifetime of an object or service time. BibTex ; Full citation; Abstract. Background. In this section, we consider a real data set on breaking stress of carbon fibres of 50 mm length (GPa) to assess the flexibility of the GR-TNB distribution over some well-known generalizations of Rayleigh distribution. Using the quadratic rank transmutation map method proposed by Shaw et al. Siddiqui, M. M. (1961) "Some Problems Connected With Rayleigh Distributions", Hogema, Jeroen (2005) "Shot group statistics", 10.1002/(sici)1098-1098(1999)10:2<109::aid-ima2>3.0.co;2-r, "A mathematical function for the description of nutrient-response curve", https://en.wikipedia.org/w/index.php?title=Rayleigh_distribution&oldid=991753095, Wikipedia articles needing page number citations from April 2013, Articles with unsourced statements from April 2013, Articles lacking in-text citations from April 2013, Creative Commons Attribution-ShareAlike License, This page was last edited on 1 December 2020, at 17:22. The Rayleigh distribution has wide range of applications in Applied Sciences; some of which are related to sea waves, harbor, coastal-engineering and studies on wind-wave heights among others. Jiju Gillariose. A second example of the distribution arises in the case of random complex numbers whose real and imaginary components are independently and identically distributed Gaussian with equal variance and zero mean. Inferential procedures on a generalized Rayleigh variate (II). Weighted Generalized Rayleigh distribution, Hoffman and Karst [10] properties of the Rayleigh distribution and applications of Rayleigh distribution to the analysis of the responses of marine vehicles to wave excitation.

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