Exponentiated distributions

This book contains completely new results, not found anywhere else. Furthermore, additional results scattered elsewhere in the literature are clearly presented. Several well-known distributions, such as Weibull distributions, Burr type XII exponential distributions, and exponential distributions, an...

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Main Author: AL-Hussaini, Essam K.,
Other Authors: Ahsanullah, Mohammad,, SpringerLink (Online service)
Format: eBook
Language: English
Bengali
Published: Paris : Atlantis Press, 2015.
Physical Description: 1 online resource (xiii, 139 pages) : color illustrations.
Series: Atlantis studies in probability and statistics ; volume 5.
Subjects:
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100 1 |a AL-Hussaini, Essam K.,  |e author. 
245 1 0 |a Exponentiated distributions /  |c Essam K. AL-Hussaini, Mohammad Ahsanullah. 
264 1 |a Paris :  |b Atlantis Press,  |c 2015. 
300 |a 1 online resource (xiii, 139 pages) :  |b color illustrations. 
336 |a text  |b txt  |2 rdacontent. 
337 |a computer  |b c  |2 rdamedia. 
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490 1 |a Atlantis Studies in Probability and Statistics,  |x 1879-6893 ;  |v volume 5. 
504 |a Includes bibliographical references. 
588 0 |a Online resource; title from PDF title page (SpringerLink, viewed January 28, 2015). 
505 0 |6 880-01  |a Class of exponential distributions Introduction - Basic properties, estimation and prediction under exponential distributions - Family of exponential Weibull distributions - Family of exponential exponential distributions - Family of type Xii exponential distributions - Finite mixture of exponential distributions. 
520 |a This book contains completely new results, not found anywhere else. Furthermore, additional results scattered elsewhere in the literature are clearly presented. Several well-known distributions, such as Weibull distributions, Burr type XII exponential distributions, and exponential distributions, and their properties are demonstrated. Both real and simulated data are analyzed. A series of inferences based on a finite mixture of distributions are also presented. 
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650 1 0 |a Statistics. 
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650 2 4 |a Statistics, general. 
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653 0 0 |a statistische analyse. 
653 0 0 |a statistical analysis. 
653 1 0 |a Statistics (General) 
653 1 0 |a Statistiek (algemeen) 
700 1 |a Ahsanullah, Mohammad,  |e author. 
710 2 |a SpringerLink (Online service) 
776 0 8 |i Printed edition:  |z 9789462390782. 
830 0 |a Atlantis studies in probability and statistics ;  |v volume 5. 
880 0 0 |6 505-01/(S  |g Machine generated contents note:  |g 1.  |t Class of Exponentiated Distributions Introduction --  |g 1.1.  |t Historical Note and Preview --  |g 1.2.  |t Generalized Order Statistics --  |g 1.3.  |t Why Use Asymmetric Loss Functions--  |g 1.4.  |t Markov Chain Monte Carlo (MCMC) Method --  |g 1.5.  |t Bayes Prediction --  |g 1.6.  |t Mixtures of Exponentiated Distribution Functions --  |t References --  |g 2.  |t Basic Properties, Estimation and Prediction Under Exponentiated Distributions --  |g 2.1.  |t Introduction --  |g 2.2.  |t Properties of the Exponentiated Class of Distributions --  |g 2.2.1.  |t Moments --  |g 2.2.2.  |t Quantiles --  |g 2.2.3.  |t Mode --  |g 2.2.4.  |t Hazard Rate Function --  |g 2.2.5.  |t Proportional Reversed Hazard Rate Function --  |g 2.2.6.  |t Density Function of the rth m-Generalized Order Statistic --  |g 2.3.  |t Estimation of Ü, R(x0), n(x0) (All Parameters of G are Known) --  |g 2.3.1.  |t Maximum Likelihood Estimation of Ü, R(x0), n(x0) --  |g 2.3.2.  |t Bayes Estimation of Ü, R(x0), n(x0) --  |g 2.4.  |t Estimation of (Ü, Ý1 ..., Ýk), RH(x0) and nH(x0) (All Parameters of H are Unknown) --  |g 2.4.1.  |t Maximum Likelihood Estimation of (Ü, Ý1 ..., Ýk), RH(x0), nH(x0) --  |g 2.4.2.  |t Bayes Estimation of (Ü, Ý1 ..., Ýk), RH(x0), nH(x0) --  |g 2.5.  |t Bayes One-Sample Prediction of Future Observables (All Parameters of H are Unknown) --  |g 2.5.1.  |t One-Sample Scheme --  |g 2.6.  |t Numerical Computations Applied to Three Examples --  |t References --  |g 3.  |t Family of Exponentiated Weibull Distributions --  |g 3.1.  |t Introduction --  |g 3.2.  |t Properties of the Exponentiated Weibull Family --  |g 3.2.1.  |t Moments --  |g 3.2.2.  |t Mean Residual Life (MRL) Function --  |g 3.2.3.  |t Quantiles --  |g 3.2.4.  |t Modes --  |g 3.2.5.  |t Hazard Rate Function --  |g 3.2.6.  |t Proportional Reversed Hazard Rate Function --  |g 3.2.7.  |t Density Function of the rth m-Generalized Order Statistic --  |g 3.3.  |t Estimation of Ü, Ý1, Ý2, RH(x0) and nH(x0), (Allparameters are Unknown) --  |g 3.3.1.  |t Maximum Likelihood Estimation --  |g 3.3.2.  |t Fisher Information Matrix --  |g 3.3.3.  |t Bayes Estimation of Ü, Ý1, Ý2, RH(x0), n(x0) --  |g 3.4.  |t Bayes Prediction of Future Observables --  |g 3.5.  |t Related Distributions to the EW Family --  |g 3.6.  |t Applications --  |t References --  |g 4.  |t Family of Exponentiated Exponential Distribution --  |g 4.1.  |t Introduction --  |g 4.2.  |t Stress-Strength Reliability --  |g 4.3.  |t Entropy --  |g 4.4.  |t Moments and Cumulants --  |g 4.5.  |t Generalized Order Statistics --  |g 4.6.  |t Distributions of Sums S2 --  |g 4.6.1.  |t Distribution of the Sum Sn --  |g 4.7.  |t Distribution of the Product and the Ratio --  |g 4.8.  |t Maximum Likelihood Estimation --  |g 4.9.  |t Characterization --  |t References --  |g 5.  |t Family of Exponentiated Burr Type XII Distributions --  |g 5.1.  |t Introduction --  |g 5.2.  |t Properties of the Exponentiated Burr XII Distributions --  |g 5.2.1.  |t Moments --  |g 5.2.2.  |t Mean Residual Life Function --  |g 5.2.3.  |t Quantiles --  |g 5.2.4.  |t Mode --  |g 5.2.5.  |t HRF --  |g 5.2.6.  |t Proportional Reversed Hazard Rate Function --  |g 5.2.7.  |t Density Function of the rth m-Generalized Order Statistic --  |g 5.3.  |t Estimation: All Parameters of H are Unknown --  |g 5.3.1.  |t Maximum Likelihood Estimation of (Ü, Ý1, Ý2), RH(x0), nH(x0) --  |g 5.3.2.  |t Bayes Estimation of (Ü, Ý1, Ý2), RH(x0), nH(x0) --  |g 5.4.  |t Prediction of Future Observables --  |g 5.4.1.  |t Random Sample Size --  |g 5.5.  |t On Beta---Burr XII Distribution --  |t References --  |g 6.  |t Finite Mixture of Exponentiated Distributions --  |g 6.1.  |t Introduction --  |g 6.2.  |t Properties of Finite Mixtures --  |g 6.2.1.  |t Moments --  |g 6.2.2.  |t MRLF --  |g 6.2.3.  |t HRF --  |g 6.2.4.  |t PRHRF --  |g 6.3.  |t Point Estimation Based on Balanced Square Error Loss Function --  |g 6.3.1.  |t Maximum Likelihood Estimation --  |g 6.3.2.  |t Bayes Estimation --  |g 6.4.  |t Numerical Example --  |g 6.4.1.  |t Point Estimation of the Parameters, SF and HRF --  |g 6.4.2.  |t Interval Estimation of the Parameters. 
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