Estimation of Survival Function for Rayleigh Distribution by Ranking function:-

In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast.

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Bayesian Estimation of the Parameter of the p-Dimensional Size-Biased Rayleigh Distribution

Lietuvos statistikos darbai ◽

10.15388/ljs.2017.13675 ◽

2017 ◽

Vol 56 (1) ◽

pp. 88-91

Author(s):

Arun Kumar Rao ◽

Himanshu Pandey ◽

Kusum Lata Singh

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Bayesian Estimation ◽

Density Function ◽

Rayleigh Distribution ◽

Survival Model ◽

Loss Functions ◽

Bayes Estimators ◽

Hazard Functions ◽

Squared Error

In this paper, we have derived the probability density function of the size-biased p-dimensional Rayleigh distribution and studied its properties. Its suitability as a survival model has been discussed by obtaining its survival and hazard functions. We also discussed Bayesian estimation of the parameter of the size-biased p-dimensional Rayleigh distribution. Bayes estimators have been obtained by taking quasi-prior. The loss functions used are squared error and precautionary.

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On a new distribution based on the arccosine function

Arabian Journal of Mathematics ◽

10.1007/s40065-021-00337-x ◽

2021 ◽

Author(s):

Christophe Chesneau ◽

Lishamol Tomy ◽

Jiju Gillariose

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Density Function ◽

Hazard Rate ◽

Survival Function ◽

Real Data ◽

Cumulative Distribution ◽

Data Sets ◽

Power Functions ◽

New Distribution

AbstractThis note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this distribution has the exact inverse cosine function as a probability density function. To our knowledge, despite obvious mathematical interest, such a probability density function has never been considered in Probability and Statistics. Here, we fill this gap by pointing out the main properties of the proposed distribution, from both the theoretical and practical aspects. Specifically, we provide the analytical form expressions for its cumulative distribution function, survival function, hazard rate function, raw moments and incomplete moments. The asymptotes and shape properties of the probability density and hazard rate functions are described, as well as the skewness and kurtosis properties, revealing the flexible nature of the new distribution. In particular, it appears to be “round mesokurtic” and “left skewed”. With these features in mind, special attention is given to find empirical applications of the new distribution to real data sets. Accordingly, the proposed distribution is compared with the well-known power distribution by means of two real data sets.

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Alpha Power Transformed Lindley Distribution

ICSA - International Conference on Statistics and Analytics 2019 ◽

10.29244/icsa.2019.pp130-142 ◽

2021 ◽

pp. 130-142

Author(s):

L A Rosa ◽

S Nurrohmah ◽

I Fithriani

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Density Function ◽

Hazard Rate ◽

Survival Function ◽

Cumulative Distribution ◽

Likelihood Method ◽

Alpha Power ◽

Lindley Distribution ◽

Modelling Data

The one parameter Lindley distribustion (theta) has been widely used in various field such as biology, technique, medical, and industries. Lindley distribution is capable for modelling data with monotone increasing hazard rate. However, in real life, there are situations where the hazard rate is not monotone. Therefore, to enhance the Lindley distribution capabilitiesfor modelling data, a modification can be used by using Alpha Power Transformed method. The result of the modification of Lindley distribution is commonly called Alpha Power Transformed Lindley distribution (APTL) distribution that has two parameters (alpha, theta). This new APTL distribution is appropriate in modelling data with decreasing or unimodal shaped of probability density function, and has hazard rates with increasing, decreasing, and upside-down bathtub shaped. The properties of the proposed distribution are discussed include probability density function, cumulative distribution function, survival function, hazard rate function, moment generating function, and rth moment. Themodel parameters are obtained using maximum likelihood method. The waiting time data is used as an illustration to describe the utility of APTL distribution.

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