scholarly journals Theoretical Description Of A Reparamatrization of Discrete Two Parameter Poisson Lindley Distribution for Modeling Waiting And Survival Times Data

2016 ◽  
Vol 29 (1) ◽  
pp. 217-222
Author(s):  
Tanka Raj Adhikari
Keyword(s):  
Poisson Distribution ◽  
Method Of Moments ◽  
Research Paper ◽  
Theoretical Description ◽  
Survival Times ◽  
Lindley Distribution ◽  
Two Parameters ◽  
First Four Moments ◽  
Special Case ◽  
Two Parameter

In this research paper, the theoretical description of are paramatrization of a discrete two-parameter Poisson Lindley Distribution, of which Sankaran’s (1970) one parameter Poisson Lindley Distribution is a special case, is derived by compounding a Poisson Distribution with two parameters Lindley Distribution for modeling waiting and survival times data of Shanker et al. (2012).The first four moments of this distribution have derived. Estimation of the parameters by using method of moments and maximum likely hood method has been discussed.

scholarly journals A Generalised Exponential-Lindley Mixture of Poisson Distribution

2019 ◽  
Vol 3 ◽  
pp. 11-20
Author(s):  
Binod Kumar Sah ◽  
A. Mishra
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Mixture Distribution ◽  
Discrete Data ◽  
Likelihood Method ◽  
P Value ◽  
Data Set ◽  
Lindley Distribution ◽  
First Four Moments

Background: The exponential and the Lindley (1958) distributions occupy central places among the class of continuous probability distributions and play important roles in statistical theory. A Generalised Exponential-Lindley Distribution (GELD) was given by Mishra and Sah (2015) of which, both the exponential and the Lindley distributions are the particular cases. Mixtures of distributions form an important class of distributions in the domain of probability distributions. A mixture distribution arises when some or all the parameters in a probability function vary according to certain probability law. In this paper, a Generalised Exponential- Lindley Mixture of Poisson Distribution (GELMPD) has been obtained by mixing Poisson distribution with the GELD. Materials and Methods: It is based on the concept of the generalisations of some continuous mixtures of Poisson distribution. Results: The Probability mass of function of generalized exponential-Lindley mixture of Poisson distribution has been obtained by mixing Poisson distribution with GELD. The first four moments about origin of this distribution have been obtained. The estimation of its parameters has been discussed using method of moments and also as maximum likelihood method. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature and it has been observed that the distribution gives a better fit than the Poisson–Lindley Distribution (PLD) of Sankaran (1970). Conclusion: P-value of the GELMPD is found greater than that in case of PLD. Hence, it is expected to be a better alternative to the PLD of Sankaran for similar type of discrete data-set which is negative binomial in nature.

scholarly journals Characterizations of Twenty (2020-2021) Proposed Discrete Distributions

2021 ◽  
pp. 847-884
Author(s):  
G.G. Hamedani ◽  
Mahrokh Najaf ◽  
Amin Roshani ◽  
Nadeem Shafique Butt
Keyword(s):  
Exponential Distribution ◽  
Poisson Distribution ◽  
Geometric Distribution ◽  
Discrete Distribution ◽  
Gumbel Distribution ◽  
Rayleigh Distribution ◽  
Discrete Distributions ◽  
Lindley Distribution ◽  
Lomax Distribution ◽  
Two Parameter

In this paper, certain characterizations of twenty newly proposed discrete distributions: the discrete gen- eralized Lindley distribution of El-Morshedy et al.(2021), the discrete Gumbel distribution of Chakraborty et al.(2020), the skewed geometric distribution of Ong et al.(2020), the discrete Poisson X gamma distri- bution of Para et al.(2020), the discrete Cos-Poisson distribution of Bakouch et al.(2021), the size biased Poisson Ailamujia distribution of Dar and Para(2021), the generalized Hermite-Genocchi distribution of El-Desouky et al.(2021), the Poisson quasi-xgamma distribution of Altun et al.(2021a), the exponentiated discrete inverse Rayleigh distribution of Mashhadzadeh and MirMostafaee(2020), the Mlynar distribution of Fr¨uhwirth et al.(2021), the flexible one-parameter discrete distribution of Eliwa and El-Morshedy(2021), the two-parameter discrete Perks distribution of Tyagi et al.(2020), the discrete Weibull G family distribution of Ibrahim et al.(2021), the discrete Marshall–Olkin Lomax distribution of Ibrahim and Almetwally(2021), the two-parameter exponentiated discrete Lindley distribution of El-Morshedy et al.(2019), the natural discrete one-parameter polynomial exponential distribution of Mukherjee et al.(2020), the zero-truncated discrete Akash distribution of Sium and Shanker(2020), the two-parameter quasi Poisson-Aradhana distribution of Shanker and Shukla(2020), the zero-truncated Poisson-Ishita distribution of Shukla et al.(2020) and the Poisson-Shukla distribution of Shukla and Shanker(2020) are presented to complete, in some way, the au- thors’ works.

scholarly journals Zero-Truncated Discrete Two-Parameter Poisson-Lindley Distribution with Applications

2018 ◽  
Vol 22 (2) ◽  
pp. 76-85
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Lindley Distribution ◽  
Coefficients Of Variation ◽  
And Behavior ◽  
Two Parameter

A zero-truncated discrete two-parameter Poisson-Lindley distribution (ZTDTPPLD), which includes zero-truncated Poisson-Lindley distribution (ZTPLD) as a particular case, has been introduced. The proposed distribution has been obtained by compounding size-biased Poisson distribution (SBPD) with a continuous distribution. Its raw moments and central moments have been given. The coefficients of variation, skewness, kurtosis, and index of dispersion have been obtained and their nature and behavior have been studied graphically. Maximum likelihood estimation (MLE) has been discussed for estimating its parameters. The goodness of fit of ZTDTPPLD has been discussed with some data sets and the fit shows satisfactory over zero – truncated Poisson distribution (ZTPD) and ZTPLD. Journal of Institute of Science and TechnologyVolume 22, Issue 2, January 2018, Page: 76-85

scholarly journals A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data

2013 ◽  
Vol 04 (02) ◽  
pp. 363-368 ◽  
Author(s):  
Rama Shanker ◽  
Shambhu Sharma ◽  
Ravi Shanker
Keyword(s):  
Survival Times ◽  
Lindley Distribution ◽  
Two Parameter

Two parameters are required for a Budyko function to describe the land-atmosphere interaction

2021 ◽  
Author(s):  
Daeha Kim ◽  
Jong Ahn Chun
Keyword(s):  
Land Surface ◽  
River Basins ◽  
Control Surface ◽  
Primary Control ◽  
Evaporative Demand ◽  
Atmosphere Interaction ◽  
The Mean ◽  
Two Parameters ◽  
Two Parameter ◽  
Surface Changes

<p>While the Budyko framework has been a simple and convenient tool to assess runoff (Q) responses to climatic and surface changes, it has been unclear how parameters of a Budyko function represent the vertical land-atmosphere interactions. Here, we explicitly derived a two-parameter equation by correcting a boundary condition of the Budyko hypothesis. The correction enabled for the Budyko function to reflect the evaporative demand (E<sub>p</sub>) that actively responds to soil moisture deficiency. The derived two-parameter function suggests that four physical variables control surface runoff; namely, precipitation (P), potential evaporation (E<sub>p</sub>), wet-environment evaporation (E<sub>w</sub>), and the catchment properties (n). We linked the derived Budyko function to a definitive complementary evaporation principle, and assessed the relative elasticities of Q to climatic and land surface changes. Results showed that P is the primary control of runoff changes in most of river basins across the world, but its importance declined with climatological aridity. In arid river basins, the catchment properties play a major role in changing runoff, while changes in E<sub>p</sub> and E<sub>w</sub> seem to exert minor influences on Q changes. It was also found that the two-parameter Budyko function can capture unusual negative correlation between the mean annual Q and E<sub>p</sub>. This work suggests that at least two parameters are required for a Budyko function to properly describe the vertical interactions between the land and the atmosphere.</p>

The Maple Syrup Problem Revisited: MCMC with Gibbs Sampling

2019 ◽  
pp. 247-266
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Monte Carlo ◽  
Gibbs Sampling ◽  
Posterior Distribution ◽  
Unknown Parameter ◽  
The Other ◽  
Sampling Step ◽  
Maple Syrup ◽  
Two Parameters ◽  
Special Case ◽  
Joint Posterior Distribution

This chapter introduces Markov Chain Monte Carlo (MCMC) with Gibbs sampling, revisiting the “Maple Syrup Problem” of Chapter 12, where the goal was to estimate the two parameters of a normal distribution, μ‎ and σ‎. Chapter 12 used the normal-normal conjugate to derive the posterior distribution for the unknown parameter μ‎; the parameter σ‎ was assumed to be known. This chapter uses MCMC with Gibbs sampling to estimate the joint posterior distribution of both μ‎ and σ‎. Gibbs sampling is a special case of the Metropolis–Hastings algorithm. The chapter describes MCMC with Gibbs sampling step by step, which requires (1) computing the posterior distribution of a given parameter, conditional on the value of the other parameter, and (2) drawing a sample from the posterior distribution. In this chapter, Gibbs sampling makes use of the conjugate solutions to decompose the joint posterior distribution into full conditional distributions for each parameter.

scholarly journals A Bayesian Approach for Estimating Parameter of Rayleigh Distribution

2019 ◽  
Vol 11 (1) ◽  
pp. 23-39
Author(s):  
J. Mahanta ◽  
M. B. A. Talukdar
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Bayesian Approach ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Risk ◽  
Squared Error ◽  
Different Types ◽  
Two Parameters ◽  
Special Case

This paper is concerned with estimating the parameter of Rayleigh distribution (special case of two parameters Weibull distribution) by adopting Bayesian approach under squared error (SE), LINEX, MLINEX loss function. The performances of the obtained estimators for different types of loss functions are then compared. Better result is found in Bayesian approach under MLINEX loss function. Bayes risk of the estimators are also computed and presented in graphs.

scholarly journals Quantal and graded dose-responses of bluetongue virus: a comparison of their sensitivity as assay methods for neutralizing antibody

1966 ◽  
Vol 64 (2) ◽  
pp. 231-244 ◽  
Author(s):  
Sven-Eric Svehag
Keyword(s):  
Poisson Distribution ◽  
Bluetongue Virus ◽  
Neutralizing Antibody ◽  
Survival Times ◽  
Response Curves ◽  
Virus Particles ◽  
The Best Approximation ◽  
Graded Responses ◽  
Quantal Responses ◽  
Random Variation

The sensitivity of quantal and graded responses to mouse-adapted bluetongue virus for the detection of neutralizing antibody was compared using probit and rankit analysis. The graded response, based on survival times, allowed the demonstration of antibody in highly dilute serum, in which antibody was not detected by the quantal response recording percentage death.Quantal responses to bluetongue virus variants were compared with theoretical dose-response curves constructed according to the Poisson distribution for the random variation of virus particles in inocula. Of these theoretical curves the first term in the Poisson distribution gave the best approximation to the experimental data but the fit to normal distribution curves was better. The quantal responses to bluetongue virus did not appear to reflect the random variation of one-or-more infectious virus particles in inocula.In graded responses to bluetongue virus, a rectilinear relationship was observed between reciprocal harmonic means of survival times and log virus dilutions.

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