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Weibull distribution

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Journal Article

A study of time spectrum identification of induced polarization field based on Weibull distribution function

Qingxin Meng, Wenli Gao, Zheng Niu, Jianghao Chang, Shida Sun, Haibo Zhang
Journal: Geophysics
Published: 08 September 2022
Geophysics (2022) 87 (6): JM41–JM54.
DOI: https://doi.org/10.1190/geo2021-0622.1
... be difficult to implement stably due to the lack of objective reference for the optimal solution. Therefore, our purpose is to improve the forward model and implement the spectrum identification for IP data. First, using the Weibull (WB) distribution function as the basis, a time spectrum forward model...
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Journal Article

Weibull vs. Lognormal Distributions for Fluvial Gravels

G.M. Kondolf, A. Adhikari
Published: 01 May 2000
Journal of Sedimentary Research (2000) 70 (3): 456–460.
DOI: https://doi.org/10.1306/2DC4091E-0E47-11D7-8643000102C1865D
... be illuminated somewhat by recognizing that the Rosin distribution is the same as the well-studied Weibull distribution. However, it can be difficult to distinguish the lognormal, Rosin (Weibull), and even gamma distributions in particle size distribution curves. Brennan and Durrett (1987) suggest...
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Weibull distribution with different shape parameters (β). (a) Weibull PDFs plotted with same scale parameter η but different β shape parameters. CV indicated. (b) Hazard‐rate functions for the PDFs shown in panel (a). The color version of this figure is available only in the electronic edition.

Weibull distribution with different shape parameters ( β ). (a) Weibull...

Published: 27 December 2022
Figure 7. Weibull distribution with different shape parameters ( β ). (a) Weibull PDFs plotted with same scale parameter η but different β shape parameters. CV indicated. (b) Hazard‐rate functions for the PDFs shown in panel (a). The color version of this figure is available only
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Distribution function of Weibull distribution.

Distribution function of Weibull distribution.

Published: 30 July 2022
Figure 7 Distribution function of Weibull distribution.
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The density function of the Weibull distribution.

The density function of the Weibull distribution.

Published: 30 July 2022
Figure 6 The density function of the Weibull distribution.
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Random heterogeneous rock specimens constructed by Weibull distribution (a) and GBM (b). (a) The simulation model in the work of Ke et al. [10]. Mechanical parameters of each small element obey the Weibull distribution. (b) The generated random grains in the work of Li et al. [16]. Balls are grouped into different minerals according Voronoi polygon (blue line).

Random heterogeneous rock specimens constructed by Weibull distribution (a)...

Published: 19 July 2022
Figure 1 Random heterogeneous rock specimens constructed by Weibull distribution (a) and GBM (b). (a) The simulation model in the work of Ke et al. [ 10 ]. Mechanical parameters of each small element obey the Weibull distribution. (b) The generated random grains in the work of Li et al. [ 16
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Weibull distribution of holding time (Table 2) with different parameters for flexible congestion modeling.

Weibull distribution of holding time ( Table 2 ) with different parameters ...

Published: 01 November 2021
Figure 2. Weibull distribution of holding time ( Table 2 ) with different parameters for flexible congestion modeling.
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Density function of Weibull distributions for each parameters. (a) Density function of Weibull distributions for different m. (b) Density function of Weibull distributions for different F. (c) Density function of Weibull distributions for different γ.

Density function of Weibull distributions for each parameters. (a) Density ...

Published: 05 May 2022
Figure 1 Density function of Weibull distributions for each parameters. (a) Density function of Weibull distributions for different m . (b) Density function of Weibull distributions for different F . (c) Density function of Weibull distributions for different γ .
Journal Article

Investigation on the Expression Ability of a Developed Constitutive Model for Rocks Based on Statistical Damage Theory

Meiben Gao, Shenghua Cui, Tianbin Li, Chunchi Ma, Zhongteng Wu, Yan Zhang, Yang Gao, Zhe Fu, Yuyi Zhong
Journal: Lithosphere
Publisher: GSW
Published: 05 May 2022
Lithosphere (2021) 2021 (Special 7): 9874408.
DOI: https://doi.org/10.2113/2022/9874408
...Figure 1 Density function of Weibull distributions for each parameters. (a) Density function of Weibull distributions for different m . (b) Density function of Weibull distributions for different F . (c) Density function of Weibull distributions for different γ . ...
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Comparisons of Weibull and LTFM. (a) Pallett Creek interevent time cumulative hazard plot for Weibull distribution with 1σ uncertainties of the interevent times indicated. (b) Comparison of best‐fitting Weibull distribution and β=2 Weibull distribution to the long‐run LTFM‐LR interevent time distribution. Interevent time mean (μ) and standard deviation (σ) are indicated. (c) Corresponding hazard‐rate functions for PDFs in panel (b). The color version of this figure is available only in the electronic edition.

Comparisons of Weibull and LTFM. (a) Pallett Creek interevent time cumulati...

Published: 27 December 2022
Figure 8. Comparisons of Weibull and LTFM. (a) Pallett Creek interevent time cumulative hazard plot for Weibull distribution with 1 σ uncertainties of the interevent times indicated. (b) Comparison of best‐fitting Weibull distribution and β = 2 Weibull distribution to the long‐run
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Comparison of gamma and Weibull distributions for spatial variability at two values of position. These examples are for AD and are independent of magnitude. These distributions are used to ultimately obtain a distribution for displacement.

Comparison of gamma and Weibull distributions for spatial variability at tw...

Published: 01 August 2011
Figure 4. Comparison of gamma and Weibull distributions for spatial variability at two values of position. These examples are for AD and are independent of magnitude. These distributions are used to ultimately obtain a distribution for displacement.
Journal Article

Simulation-Based Distributions of Earthquake Recurrence Times on the San Andreas Fault System

Gleb Yakovlev, Donald L. Turcotte, John B. Rundle, Paul B. Rundle
Published: 01 December 2006
Bulletin of the Seismological Society of America (2006) 96 (6): 1995–2007.
DOI: https://doi.org/10.1785/0120050183
... accumulation and the strength of the fault. Very few faults have a recorded history of earthquakes that define a distribution well. For hazard assessment, in general, a statistical distribution of recurrence times is assumed along with parameter values. Assumed distributions include the Weibull (stretched...
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View PDF for article title, Simulation-Based <span class="search-highlight">Distributions</span> of Earthquake Recurrence Times on the San Andreas Fault System
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Parameters of Weibull distributions for interarrival times ( i ), holding t...

Published: 01 November 2021
Table 2. Parameters of Weibull distributions for interarrival times ( i ), holding times ( h ), and retrial attempts ( r ) in the congestion model for a central office in Shelby County Source PGA * Interarrival time ( i ) Holding time ( h ) Retrial attempts ( r ) α i
Journal Article

Recurrence Time Distributions of Large Earthquakes in a Stochastic Model for Coupled Fault Systems: The Role of Fault Interaction

G. Zöller, S. Hainzl
Published: 01 October 2007
Bulletin of the Seismological Society of America (2007) 97 (5): 1679–1687.
DOI: https://doi.org/10.1785/0120060262
..., the recurrence time distribution of earthquakes on one fault follows mostly the Brownian passage-time distribution. For a strongly coupled system, the faults are synchronized and the effect of instantaneous triggering becomes dominant: the recurrence time distribution follows a Gamma or a Weibull distribution...
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Journal Article

The paradox of the expected time until the next earthquake

D. Sornette, L. Knopoff
Published: 01 August 1997
Bulletin of the Seismological Society of America (1997) 87 (4): 789–798.
DOI: https://doi.org/10.1785/BSSA0870040789
.... The periodic, uniform, semi-Gaussian, Rayleigh, and truncated statistical distributions of interval times, as well as the Weibull distributions with exponent greater than 1, all have decreasing expected time to the next earthquake with increasing time since the last one, for long times since the last...
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Lognormal, Weibull, and normal model frequency distributions for normalized recurrence interval (all curves are normalized to the mean recurrence interval). The lognormal(N) and Weibull distributions are the best‐fit model for the seven faults presented in Figure 6 of Nicol, Robinson, et al. (2016) and the lognormal(B) model from Biasi et al. (2015) for the southern Alpine fault. The more strongly time‐predictable normal distribution has a mean NET of 1 and a standard deviation of 0.33, with the maximum and the minimum values being approximately defined by extreme values in the paleoearthquake data (Table S1). The lognormal(N) and Weibull distributions are strongly positively skewed and only slightly more time predictable than a random (exponential) distribution. Refer to Table 1 for model distribution parameters.

Lognormal, Weibull, and normal model frequency distributions for normalized...

Published: 16 January 2024
Figure 4. Lognormal, Weibull, and normal model frequency distributions for normalized recurrence interval (all curves are normalized to the mean recurrence interval). The lognormal( N ) and Weibull distributions are the best‐fit model for the seven faults presented in Figure 6 of Nicol, Robinson
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Effects of future time interval Δt on TD‐SPSHA‐RJ: Comparison of the hazard curves with different Δt using (a) normal, (c) lognormal, (e) gamma, (g) BPT, and (i) Weibull distribution as the renewal model. Ratio of TD‐SPSHA with different Δt to TID‐SPSHA using (b) normal, (d) lognormal, (f) gamma, (h) BPT, and (j) Weibull distribution as the renewal model (Mmax=7, Rrup=10  km, vE,NC=0.144, renewal model: normal, lognormal, gamma, BPT, Weibull). The color version of this figure is available only in the electronic edition.

Effects of future time interval Δ t on TD‐SPSHA‐RJ: Comparison of th...

Published: 27 December 2023
Figure 10. Effects of future time interval Δ t on TD‐SPSHA‐RJ: Comparison of the hazard curves with different Δ t using (a) normal, (c) lognormal, (e) gamma, (g) BPT, and (i) Weibull distribution as the renewal model. Ratio of TD‐SPSHA with different Δ t to TID‐SPSHA using (b
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An ideal Weibull cumulative frequency distribution (evaluated at forty points) plotted on a lognormally transformed scale. The dots are points drawn from the ideal Weibull distribution, with parameters drawn from example 10 in table 11 of Rosin and Rammler (1933). The straight line is the lognormal best fit. The correlation is very high: r = 0.98 (r2 = 0.96), but the relationship is clearly nonlinear.

An ideal Weibull cumulative frequency distribution (evaluated at forty poin...

Published: 01 May 2000
Figure 1 An ideal Weibull cumulative frequency distribution (evaluated at forty points) plotted on a lognormally transformed scale. The dots are points drawn from the ideal Weibull distribution, with parameters drawn from example 10 in table 11 of Rosin and Rammler (1933) . The straight line
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Example distribution parameters for spatial slip variability P(D&gt;d|m;slip). The regressions shown are valid for a Weibull distribution. Each point plotted here is a distribution parameter fit from data in the corresponding bin. The regressions are third-order polynomials in log space. These parameters are inserted into a Weibull distribution to yield the correct shape necessary to represent D/AD anywhere along the surface rupture.

Example distribution parameters for spatial slip variability P ( D > d ...

Published: 01 August 2011
Figure 3. Example distribution parameters for spatial slip variability P ( D > d | m ;slip). The regressions shown are valid for a Weibull distribution. Each point plotted here is a distribution parameter fit from data in the corresponding bin. The regressions are third-order polynomials
Journal Article

The mixture distribution models for interoccurence times of earthquakes

M. Erisoglu, N. Calis, T. Servi, U. Erisoglu, M. Topaksu
Published: 01 July 2011
Russ. Geol. Geophys. (2011) 52 (7): 737–744.
DOI: https://doi.org/10.1016/j.rgg.2011.06.007
... and Weibull distributions are the frequently used methods in this regard. In this study, we investigate the interoccurence time statistics of earthquakes which occurred in the area coordinated 39º–42º N latitude and 30º–40º E longitude in the North Anatolian Fault Zone (NAFZ) between the years 1960–2008...
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