2020 # Some New Facts about the Unit-Rayleigh Distribution with Applications

**Abstract:** The unit-Rayleigh distribution is a one-parameter distribution with support on the unit interval. It is defined as the so-called unit-Weibull distribution with a shape parameter equal to two. As a particular case among others, it seems that it has not been given special attention. This paper shows that the unit-Rayleigh distribution is much more interesting than it might at first glance, revealing closed-form expressions of important functions, and new desirable properties for application purposes. More precis…

Help me understand this report

Search citation statements

Paper Sections

Select...

3

1

1

Citation Types

0

25

0

Year Published

2021

2024

Publication Types

Select...

9

Relationship

5

4

Authors

Journals

(29 citation statements)

(21 reference statements)

0

25

0

“…Although it has very flexible forms for data modeling, sometimes it is not sufficient for modeling and explaining unit datasets. For this reason, new alternative unit models have been proposed in the statistical distribution literature, including the Johnson S B [1], Topp-Leone [2], Kumaraswamy [3], standart two-sided power [4], log-Lindley [5], log-xgamma [6], unit Birnbaum-Saunders [7], unit Weibull [8], unit Lindley [9], unit inverse Gaussian [10], unit Gompertz [11], second degree unit Lindley [12], log-weighted exponential [13], logit slash [14], unit generalized half normal [15], unit Johnson S U [16], trapezoidal beta [17] and unit Rayleigh [18] distributions. Many of the above distributions were obtained by transforming the baseline distribution, and they performed better than the beta distribution in terms of data modeling.…”

confidence: 99%

“…Although it has very flexible forms for data modeling, sometimes it is not sufficient for modeling and explaining unit datasets. For this reason, new alternative unit models have been proposed in the statistical distribution literature, including the Johnson S B [1], Topp-Leone [2], Kumaraswamy [3], standart two-sided power [4], log-Lindley [5], log-xgamma [6], unit Birnbaum-Saunders [7], unit Weibull [8], unit Lindley [9], unit inverse Gaussian [10], unit Gompertz [11], second degree unit Lindley [12], log-weighted exponential [13], logit slash [14], unit generalized half normal [15], unit Johnson S U [16], trapezoidal beta [17] and unit Rayleigh [18] distributions. Many of the above distributions were obtained by transforming the baseline distribution, and they performed better than the beta distribution in terms of data modeling.…”

confidence: 99%

“…As a main statistical work, we analyze this data set via a fitting approach. In this regard, we compare the fit of the proposed UG/G model and those of the Kumaraswamy (Kw), beta (Beta), UR (recalling that it refers to the unit Rayleigh distribution by [10]), Topp-Leone (Topp), power (Power), and Transmuted (TM) models. These competitive models are defined by specific cdfs, which are recalled below.…”

confidence: 99%

“…This particular scheme is also known to transpose some characteristics of the distribution of X to the unit interval. With this inverse-exponential scheme, we may refer the reader to the construction of the log-gamma distribution developed by [2] and based on the standard gamma distribution, log-Lindley distribution established by [3] and based on the Lindley distribution, unit Weibull distribution examined by [4,5] and using the Weibull distribution, unit Gompertz distribution developed by [6] and based on the Gompertz distribution, unit Burr-XII (UBXII) created by [7] distribution and based on the Burr-XII distribution, log-weighted exponential distribution motivated by [8] and based on the weighted exponential distribution, log-Xgamma distribution proposed by [9] and based on the Xgamma distribution, and unit Rayleigh (UR) distribution studied in [10] and using the Rayleigh distribution, among others.…”

confidence: 99%

“…Modern applications are numerous in the fields of psychology, economics, biology, and engineering. For more information on this topic, see [21][22][23][24] as well as the references therein. is section is dedicated to the unit truncated M distribution, which will be the main ingredient to the NTM-G family.…”

confidence: 99%