Statistical properties of the nonlinear negative binomial state

2007 ◽  
Vol 274 (2) ◽  
pp. 372-383 ◽  
Author(s):  
M. Sebawe Abdalla ◽  
A.-S.F. Obada ◽  
M. Darwish
Keyword(s):  
Negative Binomial ◽  
Statistical Properties ◽  
Binomial State

SOME FEATURES OF SQUEEZED NEGATIVE BINOMIAL STATE

1992 ◽  
Vol 06 (03n04) ◽  
pp. 409-415 ◽  
Author(s):  
AMITABH JOSHI ◽  
S. V. LAWANDE
Keyword(s):  
Electromagnetic Field ◽  
Density Matrix ◽  
Wigner Function ◽  
Negative Binomial ◽  
Thermal State ◽  
Photon Number ◽  
Binomial State ◽  
Relationship Of ◽  
The Relationship ◽  
Photon Number Distribution

Properties of electromagnetic field in the squeezed negative binomial state are investigated in terms of photon number distribution and Wigner function. The relationship of the density matrix of the squeezed negative binomial state to the density matrix of the squeezed thermal state is shown explicitly. The possibility of generation of the negative binomial state is also discussed.

scholarly journals Maximum Product of Spacing Parameter Estimation of Gompertz Rayleigh Distribution and Application to Rainfall Datasets

2021 ◽  
pp. 41-59
Author(s):  
Hussein Ahmad Abdulsalam ◽  
Sule Omeiza Bashiru ◽  
Alhaji Modu Isa ◽  
Yunusa Adavi Ojirobe
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Rainfall Data ◽  
Parameter Estimates ◽  
Data Sets ◽  
Unknown Parameters ◽  
Exponentiated Weibull ◽  
Integrated Hazard

Gompertz Rayleigh (GomR) distribution was introduced in an earlier study with few statistical properties derived and parameters estimated using only the most common traditional method, Maximum Likelihood Estimation (MLE). This paper aimed at deriving more statistical properties of the GomR distribution, estimating the three unknown parameters via a competitive method, Maximum Product of Spacing (MPS) and evaluating goodness of fit using rainfall data sets from Nigeria, Malaysia and Argentina. Properties of statistical distributions including distribution of smallest and largest order statistics, cumulative or integrated hazard function, odds function, rth non-central moments, moment generating function, mean, variance and entropy measures for GomR distribution were explicitly derived. The fitted data sets reveal the flexibility of GomR distribution over other distributions been compared with. Simulation study was used to evaluate the consistency, accuracy and unbiasedness of the GomR distribution parameter estimates obtained from the method of MPS. The study found that GomR distribution could not provide a better fit for Argentine rainfall data but it was the best distribution for the rainfall data sets from Nigeria and Malaysia in comparison with the distributions; Generalized Weibull Rayleigh (GWR), Exponentiated Weibull Rayleigh (EWR), Type (II) Topp Leone Generalized Inverse Rayleigh (TIITLGIR), Kumarawamy Exponential Inverse Raylrigh (KEIR), Negative Binomial Marshall-Olkin Rayleigh (NBMOR) and Exponentiated Weibull (EW). Furthermore, the estimates from MPSE were consistent as the sample size increases but not as efficient as those from MLE.

Wigner function for squeezed negative binomial state and evolution of density operator for amplitude decay

2019 ◽  
Vol 28 (9) ◽  
pp. 090302 ◽  
Author(s):  
Heng-Yun Lv ◽  
Ji-Suo Wang ◽  
Xiao-Yan Zhang ◽  
Meng-Yan Wu ◽  
Bao-Long Liang ◽  
...  
Keyword(s):  
Wigner Function ◽  
Density Operator ◽  
Negative Binomial ◽  
Binomial State

Two-Parameter Correlated Negative Binomial State in Two-Mode Fock Space

1998 ◽  
Vol 15 (7) ◽  
pp. 469-471 ◽  
Author(s):  
Hong-yi Fan ◽  
Xiao-yin Pan ◽  
Bo-zhan Chen
Keyword(s):  
Negative Binomial ◽  
Fock Space ◽  
Binomial State ◽  
Two Parameter

scholarly journals The Novel Bivariate Distribution: Statistical Properties and Real Data Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
B. I. Mohammed ◽  
Abdulaziz S. Alghamdi ◽  
Hassan M. Aljohani ◽  
Md. Moyazzem Hossain
Keyword(s):  
Negative Binomial ◽  
Real Data ◽  
Information Criterion ◽  
Mass Function ◽  
Bivariate Distribution ◽  
Statistical Properties ◽  
Model Parameters ◽  
Probability Mass Function ◽  
New Class ◽  
Probability Mass

This article proposes a novel class of bivariate distributions that are completely defined by stating their conditionals as Poisson exponential distributions. Numerous statistical properties of this distribution are also examined here, including the conditional probability mass function (PMF) and moments of the new class. The techniques of maximum likelihood and pseudolikelihood are used to estimate the model parameters. Additionally, the effectiveness of the bivariate Poisson exponential conditional (BPEC) distribution is compared to that of the bivariate Poisson conditional (BPC), the bivariate Poisson (BP), the bivariate Poisson–Lindley (BPL), and the bivariate negative binomial (BNB) distributions using a real-world dataset. The findings of Akaike information criterion (AIC) and Bayesian information criterion (BIC) reveal that the BPEC distribution performs better than the other distributions considered in this study. As a result, the authors claim that this distribution may be used to fit dependent and overspread count data.

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