scholarly journals Probability distribution of (Schwämmle and Tsallis) two-parameter entropies and the Lambert -function

2008 ◽  
Vol 387 (25) ◽  
pp. 6277-6283 ◽  
Author(s):  
Somayeh Asgarani ◽  
Behrouz Mirza
Keyword(s):  
Probability Distribution ◽  
Lambert Function ◽  
Two Parameter

Distribution of the supremum of the two-parameter Yeh-Wiener process on the boundary

1973 ◽  
Vol 10 (04) ◽  
pp. 875-880 ◽  
Author(s):  
S. R. Paranjape ◽  
C. Park
Keyword(s):  
Lower Bound ◽  
Probability Distribution ◽  
Wiener Process ◽  
Two Parameter

Let D = [0, S] × [0, T] be a rectangle in E2 and X(s, t), (s, t)∈D, be a two parameter Yeh-Wiener process. This paper finds the probability distribution of the supremum of X(s, t) on the boundary of D by taking the limit of the probability distribution of the supremum of X(s, t) along certain paths as these paths approach the boundary of D. The probability distribution of the supremum of X(s, t) on the boundary of D gives a nice lower bound for the probability distribution of the supremum of X(s, t) on D, which is unknown.

scholarly journals The Exponential-Generalized Truncated Geometric (EGTG) Distribution: A New Lifetime Distribution

2017 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
Mohieddine Rahmouni ◽  
Ayman Orabi
Keyword(s):  
Probability Distribution ◽  
Real Data ◽  
Lifetime Distribution ◽  
Data Sets ◽  
Application Study ◽  
Maximum Lifetime ◽  
Special Cases ◽  
Rate Functions ◽  
Two Parameter ◽  
New Distribution

This paper introduces a new two-parameter lifetime distribution, called the exponential-generalized truncated geometric (EGTG) distribution, by compounding the exponential with the generalized truncated geometric distributions. The new distribution involves two important known distributions, i.e., the exponential-geometric (Adamidis and Loukas, 1998) and the extended (complementary) exponential-geometric distributions (Adamidis et al., 2005; Louzada et al., 2011) in the minimum and maximum lifetime cases, respectively. General forms of the probability distribution, the survival and the failure rate functions as well as their properties are presented for some special cases. The application study is illustrated based on two real data sets.

scholarly journals Translated Logarithmic Lambert Function and its Applications to Three-Parameter Entropy

2021 ◽  
Vol 14 (2) ◽  
pp. 506-520
Author(s):  
Cristina Bordaje Corcino ◽  
Roberto Bagsarsa Corcino
Keyword(s):  
Probability Distribution ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Approximation ◽  
Taylor Series Expansion ◽  
Lambert Function

The translated logarithmic Lambert function is defined and basic analytic properties of the function are obtained including the derivative, integral, Taylor series expansion, real branches and asymptotic approximation of the function. Moreover, the probability distribution of the three-parameter entropy is derived which is expressed in terms of the translated logarithmic Lambert function.

Distribution of the supremum of the two-parameter Yeh-Wiener process on the boundary

1973 ◽  
Vol 10 (4) ◽  
pp. 875-880 ◽  
Author(s):  
S. R. Paranjape ◽  
C. Park
Keyword(s):  
Lower Bound ◽  
Probability Distribution ◽  
Wiener Process ◽  
Two Parameter

Let D = [0, S] × [0, T] be a rectangle in E2 and X(s, t), (s, t)∈D, be a two parameter Yeh-Wiener process. This paper finds the probability distribution of the supremum of X(s, t) on the boundary of D by taking the limit of the probability distribution of the supremum of X(s, t) along certain paths as these paths approach the boundary of D. The probability distribution of the supremum of X(s, t) on the boundary of D gives a nice lower bound for the probability distribution of the supremum of X(s, t) on D, which is unknown.

scholarly journals Estimation on Reliability Models of Bearing Failure Data

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Xia Xintao ◽  
Chang Zhen ◽  
Zhang Lijun ◽  
Yang Xiaowei
Keyword(s):  
Probability Distribution ◽  
Weibull Distribution ◽  
Normal Distribution ◽  
Distribution Model ◽  
Bearing Failure ◽  
Analysis Model ◽  
Failure Data ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Two Parameter

The failure data of bearing products is random and discrete and shows evident uncertainty. Is it accurate and reliable to use Weibull distribution to represent the failure model of product? The Weibull distribution, log-normal distribution, and an improved maximum entropy probability distribution were compared and analyzed to find an optimum and precise reliability analysis model. By utilizing computer simulation technology and k-s hypothesis testing, the feasibility of three models was verified, and the reliability of different models obtained via practical bearing failure data was compared and analyzed. The research indicates that the reliability model of two-parameter Weibull distribution does not apply to all situations, and sometimes, two-parameter log-normal distribution model is more precise and feasible; compared to three-parameter log-normal distribution model, the three-parameter Weibull distribution manifests better accuracy but still does not apply to all cases, while the novel proposed model of improved maximum entropy probability distribution fits not only all kinds of known distributions but also poor information issues with unknown probability distribution, prior information, or trends, so it is an ideal reliability analysis model with least error at present.

COMPARISON OF WEIBULL AND NORMAL PROBABILITY DISTRIBUTION OF FLEXURAL STRENGTH OF DENSE AND POROUS FIRED CLAY

2016 ◽  
Vol 78 (9) ◽  
Author(s):  
Muazu Abubakar ◽  
Muhamad Azizi Mat Yajid ◽  
Norhayati Ahmad
Keyword(s):  
Probability Distribution ◽  
Flexural Strength ◽  
Normal Distribution ◽  
Probability Distributions ◽  
Bending Test ◽  
Strength Data ◽  
Normal Probability ◽  
Distribution Parameters ◽  
Normal Probability Distribution ◽  
Two Parameter

In this research, dense and porous fired clay were produced at a firing temperature of 1300°C. The flexural strength data of the dense and the porous fired clay were determined using three point bending test. Two-parameter Weibull and normal probability distributions were used to estimate the reliability of the flexural strength data of the dense and the porous fired clay. From the result, the Weibull probability distribution scale parameter for the dense (36.31MPa) and Porous (18.85MPa) fired clay are higher than the mean strength value for the dense (33.84MPa) and the porous (17.87MPa) of the normal distribution. Distributions of flaws in the dense and the porous fired clay have a significant effect on the Weibull and normal distribution parameters. The fractured surface of the dense fired clay shows a random distribution of cracks while that of the porous fired clay shows a distribution of pores in the morphology. The normal distribution considers failure at 50% of the flexural strength data while Weibull probability distribution is failure at 62.3% of the strength data. Therefore, two-parameter Weibull is the suitable tool to model failure strength data of the dense and porous fired clay.  

Some results of the Barbier-Chalonge-Divan system of stellar classification

1966 ◽  
Vol 24 ◽  
pp. 77-90 ◽  
Author(s):  
D. Chalonge
Keyword(s):  
Early Type ◽  
Parameter System ◽  
Early Type Stars ◽  
Two Parameter

Several years ago a three-parameter system of stellar classification has been proposed (1, 2), for the early-type stars (O-G): it was an improvement on the two-parameter system described by Barbier and Chalonge (3).

Subjective Time Preference and Willingness to Pay for an Energy-Saving Durable Good

2001 ◽  
Vol 32 (3) ◽  
pp. 133-141 ◽  
Author(s):  
Gerrit Antonides ◽  
Sophia R. Wunderink
Keyword(s):  
Willingness To Pay ◽  
Energy Saving ◽  
Subjective Time ◽  
Durable Good ◽  
Discount Function ◽  
Hyperbolic Discount ◽  
The One ◽  
Two Parameter ◽  
Difference Effect ◽  
Better Than

Summary: Different shapes of individual subjective discount functions were compared using real measures of willingness to accept future monetary outcomes in an experiment. The two-parameter hyperbolic discount function described the data better than three alternative one-parameter discount functions. However, the hyperbolic discount functions did not explain the common difference effect better than the classical discount function. Discount functions were also estimated from survey data of Dutch households who reported their willingness to postpone positive and negative amounts. Future positive amounts were discounted more than future negative amounts and smaller amounts were discounted more than larger amounts. Furthermore, younger people discounted more than older people. Finally, discount functions were used in explaining consumers' willingness to pay for an energy-saving durable good. In this case, the two-parameter discount model could not be estimated and the one-parameter models did not differ significantly in explaining the data.

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