Widening valid estimation range of multilook Pareto shape parameter with closed‐form estimators

2016 ◽  
Vol 52 (17) ◽  
pp. 1486-1488 ◽  
Author(s):  
Chong Hu ◽  
Feng Luo ◽  
Linrang Zhang ◽  
Yifei Fan ◽  
Shuailin Chen
Keyword(s):  
Closed Form ◽  
Shape Parameter ◽  
Estimation Range

scholarly journals A closed-form orthotropic constitutive model for fused filament fabrication materials

2019 ◽  
Author(s):  
Ruiqi Chen ◽  
Debbie G. Senesky
Keyword(s):  
Constitutive Model ◽  
Closed Form ◽  
Elastic Constants ◽  
Complex Variable ◽  
Shape Parameter ◽  
Antiplane Shear ◽  
Fused Filament Fabrication ◽  
Effective Elastic Constants ◽  
Out Of Plane ◽  
Simulation Results

We model two common fused filament fabrication mesostructures, square and hexagonal, using an orthotropic constitutive model and derive closed-form expressions for all nine effective elastic constants. The periodic void shapes are modeled using three and four point hypotrochoid curves with a single shape parameter that controls the sharpness of the points. Using the complex variable method of elasticity, we derive the in-plane elastic constants (Exx, Eyy, Gxy, nuxy) as well as out-of-plane antiplane shear constants (Gzx and Gzy). The remaining out-of-plane elastic constants (Ezz, nuzx, nuzy) are derived by directly solving the linearelasticity equations. We compare our results by conducting unit cell simulations on both mesostructures and at various porosity values. The simulations match the closed-form expressions exactly for Ezz, nuzx, and nuzy. For the remaining elastic constants, the simulation results match the closed-form expressions better for the square mesostructure than the hexagonal mesostructure. Differences between simulation and closed-form expressions are less than 10% for porosity values less than 6% (hexagonal mesostructure) and 10% (square mesostructure) for any of the nine elastic constants.

scholarly journals On closed-form tight bounds and approximations for the median of a gamma distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0251626
Author(s):  
Richard F. Lyon
Keyword(s):  
Lower Bound ◽  
Closed Form ◽  
Lower Bounds ◽  
Gamma Distribution ◽  
Upper Bound ◽  
Entire Range ◽  
Shape Parameter ◽  
Upper And Lower Bounds ◽  
Elementary Functions ◽  
Asymptotic Analyses

The median of a gamma distribution, as a function of its shape parameter k, has no known representation in terms of elementary functions. In this work we use numerical simulations and asymptotic analyses to bound the median, finding bounds of the form 2−1/k(A + Bk), including an upper bound that is tight for low k and a lower bound that is tight for high k. These bounds have closed-form expressions for the constant parameters A and B, and are valid over the entire range of k > 0, staying between 48 and 55 percentile. Furthermore, an interpolation between these bounds yields closed-form expressions that more tightly bound the median, with absolute and relative margins to both upper and lower bounds approaching zero at both low and high values of k. These bound results are not supported with analytical proofs, and hence should be regarded as conjectures. Simple approximation expressions between the bounds are also found, including one in closed form that is exact at k = 1 and stays between 49.97 and 50.03 percentile.

A SIMPLE ESTIMATOR FOR THE WEIBULL SHAPE PARAMETER

2012 ◽  
Vol 12 (02) ◽  
pp. 395-402 ◽  
Author(s):  
MAHDI TEIMOURI ◽  
SARALEES NADARAJAH
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Closed Form ◽  
Maximum Likelihood Estimator ◽  
Shape Parameter ◽  
Scale Parameter ◽  
Maximum Likelihood Estimators ◽  
Simulation Studies ◽  
Likelihood Estimator

The Weibull distribution is the most popular model for lifetimes. However, the maximum likelihood estimators for the Weibull distribution are not available in closed form. In this note, we derive a simple, consistent, closed form estimator for the Weibull shape parameter. This estimator is independent of the Weibull scale parameter. Simulation studies show that this estimator performs as well as the maximum likelihood estimator.

Technique for Improving the Flow Rate Estimation Range by Using an Axial Flow Water Turbine Generator

2017 ◽  
Vol 137 (1) ◽  
pp. 30-35
Author(s):  
Hiroaki Narita ◽  
Makoto Saruwatari ◽  
Jun Matsui ◽  
Yasutaka Fujimoto
Keyword(s):  
Flow Rate ◽  
Axial Flow ◽  
Turbine Generator ◽  
Rate Estimation ◽  
Water Turbine ◽  
Estimation Range

Effect of Kaiser Window Shape Parameter for the Enhancement of Rotor Faults Diagnosis

2017 ◽  
Vol 10 (6) ◽  
pp. 461
Author(s):  
Mohammed-El-Amine Khodja ◽  
Ahmed Hamida Boudinar ◽  
Azeddine Bendiabdellah
Keyword(s):  
Shape Parameter ◽  
Rotor Faults ◽  
Faults Diagnosis ◽  
Kaiser Window

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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