Exponential-Type Bounds on the First-Order Marcum Q-Function

2011 ◽  
Author(s):  
Hua Fu ◽  
Pooi-Yuen Kam
Keyword(s):  
Exponential Type ◽  
First Order ◽  
Q Function

scholarly journals Tight bounds for the first order Marcum Q-function

2010 ◽  
Vol 12 (4) ◽  
pp. 293-301 ◽  
Author(s):  
Jiangping Wang ◽  
Dapeng Wu
Keyword(s):  
First Order ◽  
Q Function

Some possible q-exponential type probability distribution in the non-extensive statistical physics

2016 ◽  
Vol 30 (22) ◽  
pp. 1650252 ◽  
Author(s):  
Won Sang Chung
Keyword(s):  
Probability Distribution ◽  
Exponential Type ◽  
Statistical Physics ◽  
Probability Distributions ◽  
Type I ◽  
Quantum Harmonic Oscillator ◽  
Text Type ◽  
First Order ◽  
Gibbs Entropy ◽  
Level Problem

In this paper, we present two exponential type probability distributions which are different from Tsallis’s case which we call Type I: one given by [Formula: see text] (Type IIA) and another given by [Formula: see text] (Type IIIA). Starting with the Boltzman–Gibbs entropy, we obtain the different probability distribution by using the Kolmogorov–Nagumo average for the microstate energies. We present the first-order differential equations related to Types I, II and III. For three types of probability distributions, we discuss the quantum harmonic oscillator, two-level problem and the spin-[Formula: see text] paramagnet.

scholarly journals A generalized exponential-type estimator for population mean using auxiliary attributes

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0246947
Author(s):  
Sohail Ahmad ◽  
Muhammad Arslan ◽  
Aamna Khan ◽  
Javid Shabbir
Keyword(s):  
Exponential Type ◽  
Random Sampling ◽  
Finite Population ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Stratified Random Sampling ◽  
Population Mean ◽  
First Order ◽  
Squared Error ◽  
Class Of Estimators

In this paper, we propose a generalized class of exponential type estimators for estimating the finite population mean using two auxiliary attributes under simple random sampling and stratified random sampling. The bias and mean squared error (MSE) of the proposed class of estimators are derived up to first order of approximation. Both empirical study and theoretical comparisons are discussed. Four populations are used to support the theoretical findings. It is observed that the proposed class of estimators perform better as compared to all other considered estimator in simple and stratified random sampling.

scholarly journals A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling

2015 ◽  
Vol 38 (2) ◽  
pp. 385-397 ◽  
Author(s):  
Javid Shabbir ◽  
Sat Gupta
Keyword(s):  
Exponential Type ◽  
Auxiliary Variable ◽  
Survey Sampling ◽  
Data Sets ◽  
Numerical Comparison ◽  
Order Of Approximation ◽  
Population Variance ◽  
First Order ◽  
Better Than

<p>Recently a new generalized estimator for population variance using information on the auxiliary variable has been introduced by Asghar, Sanaullah &amp; Hanif (2014). In that paper there was some inaccuracy in the bias and MSE expressions. In this paper, we provide the correct expressions for bias and MSE of the Asghar et al. (2014) estimator, up to the first order of approximation. We also propose a new generalized exponential type estimator for population variance which performs better than the existing estimators. Four data sets are used for numerical comparison of efficiencies.</p>

scholarly journals A Generalized Class of Exponential Type Estimators for Population Mean under Systematic Sampling Using Two Auxiliary Variables

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Mursala Khan
Keyword(s):  
Exponential Type ◽  
Secondary Data ◽  
Estimation Procedure ◽  
The Other ◽  
Systematic Sampling ◽  
Auxiliary Variables ◽  
Population Mean ◽  
First Order ◽  
Class Of Estimators ◽  
The Mean

We have proposed a generalized class of exponential type estimators for population mean under the framework of systematic sampling using the knowledge of two auxiliary variables. The expressions for the mean square error of the proposed class of estimators have been corrected up to first order of approximation. Comparisons of the efficiency of the proposed class of estimators under the optimal conditions with the other existing estimators have been presented through a real secondary data. The statistical study provides strong evidence that the proposed class of estimators in survey estimation procedure results in substantial efficiency improvements over the other existing estimation approaches.

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