scholarly journals Temporal characteristics of some aftershock sequences in Bulgaria

1999 ◽  
Vol 42 (5) ◽  
Author(s):  
S. Simeonova ◽  
D. Solakov
Keyword(s):  
Maximum Likelihood ◽  
Temporal Distribution ◽  
Aftershock Sequence ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Cumulative Number ◽  
Aftershock Activity ◽  
Aftershock Sequences ◽  
Secondary Aftershock ◽  
Foreshock Activity

We apply statistical analysis to study the temporal distribution of aftershocks in aftershock sequences of five earthquakes which occurred in Bulgaria. We use the maximum likelihood method to estimate the parameters of the modified Omori formula for aftershock sequences which is directly based on a time series. We find that: the maximum likelihood estimates of the parameter p show a regional variation, with lower values of the decay rate in North Bulgaria; the modified Omori formula provides an appropriate representation of temporal variation of the aftershock activity in North Bulgaria; the aftershock sequences in South Bulgaria are best modeled by the combination of an ordinary aftershock sequence with secondary aftershock activity. A plot of the cumulative number of events versus the frequency-linearized time t clearly demonstrates a transition from aftershock to foreshock activity prior to the second 1986 Strazhitsa (North Bulgaria) earthquake.

Metric for Disassembly and Reuse Decisions: Formulation and Validation

2008 ◽  
Author(s):  
Vijitashwa Pandey ◽  
Deborah Thurston
Keyword(s):  
Maximum Likelihood ◽  
Value Function ◽  
Choice Theory ◽  
Decision Makers ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Maximum Value ◽  
Long Range Planning ◽  
The Relationship ◽  
The Value Function

Design for disassembly and reuse focuses on developing methods to minimize difficulty in disassembly for maintenance or reuse. These methods can gain substantially if the relationship between component attributes (material mix, ease of disassembly etc.) and their likelihood of reuse or disposal is understood. For products already in the marketplace, a feedback approach that evaluates willingness of manufacturers or customers (decision makers) to reuse a component can reveal how attributes of a component affect reuse decisions. This paper introduces some metrics and combines them with ones proposed in literature into a measure that captures the overall value of a decision made by the decision makers. The premise is that the decision makers would choose a decision that has the maximum value. Four decisions are considered regarding a component’s fate after recovery ranging from direct reuse to disposal. A method on the lines of discrete choice theory is utilized that uses maximum likelihood estimates to determine the parameters that define the value function. The maximum likelihood method can take inputs from actual decisions made by the decision makers to assess the value function. This function can be used to determine the likelihood that the component takes a certain path (one of the four decisions), taking as input its attributes, which can facilitate long range planning and also help determine ways reuse decisions can be influenced.

scholarly journals Robust parametric estimates of inhomogeneous experimental data

2020 ◽  
pp. 55-62
Author(s):  
V.A. Simakhin ◽  
◽  
L.G. Shamanaeva ◽  
A.E. Avdyushina ◽  
◽  
...  
Keyword(s):  
Experimental Data ◽  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Robust Estimates

In the present work, a weighed maximum likelihood method (WMLM) is proposed to obtain robust estimates for processing experimental data containing outliers. The method allows robust asymptotic unbiased and effective estimates to be obtained in the presence of not only external, but also internal asymmetric and symmetric outliers. Algorithms for obtaining robust WMLM estimates are considered at the parametric level of aprioristic uncertainty. It is demonstrated that these estimates converge to maximum likelihood estimates of an inhomogeneous sample for each distribution from the Tukey supermodel.

scholarly journals On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications

2020 ◽  
pp. 721-735
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Haitham M. Yousof ◽  
Azeem Ali ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Quarterly Earnings ◽  
Inverse Weibull Distribution

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

An application of Bayesian techniques to the genetic evaluation of growth traits in Eucalyptus globulus

1998 ◽  
Vol 28 (9) ◽  
pp. 1286-1294 ◽  
Author(s):  
F Soria ◽  
F Basurco ◽  
G Toval ◽  
L Silió ◽  
M C Rodriguez ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Eucalyptus Globulus ◽  
Maximum Likelihood Estimates ◽  
Breeding Value ◽  
Likelihood Method ◽  
Phenotypic Correlation ◽  
Data Set ◽  
Breeding Values ◽  
Bayesian Techniques ◽  
Self Pollination

A Bayesian procedure coupled with Gibbs sampling was implemented to obtain inferences about genetic parameters and breeding values for height and diameter of 7-year-old Eucalyptus globulus Labill. is described. The data set consisted of 21 708 trees from 260 open-pollinated families taken from 10 different Australian provenances, from one Spanish population, and from two clones. The trees are distributed over eight sites in the south of Spain, with 20 blocks per site. Data were corrected for heterogeneity of phenotypic variances between blocks. In the analysis, a self-pollination rate of 30% for the open-pollinated families is assumed in the relationship matrix. The posterior means (and standard deviations) of the heritabilities of height and diameter and the genetic and phenotypic correlation were 0.217 (0.014), 0.128 (0.084), 0.768 (0.028), and 0.799 (0.003). Results from the standard restricted maximum likelihood method were 0.173, 0.113, 0.759, and 0.798, respectively. Most of the discrepancy in heritability estimates from both methods can be attributed to the adjustement of residual maximum likelihood estimates to the assumed self-pollination rate, which ignores the presence of clones in the trial. The effect of the method of prediction of breeding values (best linear unbiased prediction or Bayesian techniques) on the genetic superiority of the selected trees was not important. Differences in breeding value among provenances and among families were evidenced for both traits.

scholarly journals Analysis of the Spatial and Temporal Distribution of the 2011 Earthquakes in Lake Van Area and Rupture Complexity of the Aftershock Sequence in Eastern Anatolia, Turkey

2018 ◽  
Author(s):  
Mustafa Toker
Keyword(s):  
Seismic Activity ◽  
Focal Depth ◽  
Temporal Distribution ◽  
Aftershock Sequence ◽  
Spatial And Temporal Distribution ◽  
Upper Crust ◽  
Lake Van ◽  
Spatial Clusters ◽  
Central Cluster ◽  
Aftershock Sequences

This study presents an analysis of the spatial and temporal distribution of the two large destructive earthquakes that occurred in Lake Van area on October 23, and November 9, 2011, together with the azimuth-dependent distribution of the seismic activity and microseismicity clusters after the mainshocks, associated with the complex rupture processes of their aftershock sequence. The sequence began with the magnitude Mw 7.1 earthquake of 23 October and a second destructive earthquake of Mw 5.6. The aftershock sequences of the two mainshocks were linked to the local crustal faults beneath Lake Van area, followed successively and produced unusually intense activity and significant damage in the area. The main purposes of this study are to document the spatial and temporal distribution and evolution of the October 23, 2011 aftershock hypocenters and the azimuth-dependent distribution of seismic activity, and to understand the spatial and temporal character of the aftershock sequence using the distributional and evolutional patterns of the aftershock hypocenters. A total of 10,000 aftershocks were obtained from seismic data with a high signal-to-noise ratio over collected over three years from October 23, 2011 to March 2014. These aftershocks were plotted for the time periods from November 2011 through March 2012 to March 2014 and ≈ 5000 aftershocks were retained in the depth versus distance cross-sections to detect the clusters in the first step of study (November 2011–March 2012). The focal depth distribution of the aftershock clusters, the migration of hypocenter activity and microseismicity clusters were analyzed and the distributional patterns of the detected clusters were assessed using the geometric distribution of the aftershock hypocenters. The spatial and temporal distribution of aftershocks reveal interesting key features of the deep rupture complexity of the Van earthquake: (1) most prominent aftershocks have been located in the upper crust at depths shallower than 10 km beneath ruptured area, indicating that the upper crust is brittle and seismogenic; (2) two spatial clusters have been detected at 8-10 km depths and the upward extrapolation of these clusters intersects with faults; the main cluster (60 km wide) bounded by inferred reverse faults (f3 and f4) and the central cluster (25–30 km wide) bounded by faults (f1 and f2); (3) these spatial clusters form the largest volumetric pattern of the conical-shaped cluster at depths of about 25–30 km of the azimuth-dependent rotational projections, suggesting azimuthal distributions of deep rupture characteristics; and (4) the strongest temporal cluster of microseismicity derived from temporal distribution of aftershocks has been detected within an area of about 2.5–3.0 km2 and it is spatially observed at 20 km depth within the central cluster, suggesting progressive failure of the adjacent patches of possible fault.

Background Seismicity before and after the 1976 Ms 7.8 Tangshan Earthquake: Is Its Aftershock Sequence Still Continuing?

2020 ◽  
Author(s):  
Yue Liu ◽  
Jiancang Zhuang ◽  
Changsheng Jiang
Keyword(s):  
Aftershock Sequence ◽  
Tangshan Earthquake ◽  
Aftershock Activity ◽  
Background Rate ◽  
Epidemic Type Aftershock Sequence ◽  
Aftershock Sequences ◽  
Background Seismicity ◽  
Before And After ◽  
Large Earthquakes ◽  
Current Stage

Abstract The aftershock zone of the 1976 Ms 7.8 Tangshan, China, earthquake remains seismically active, experiencing moderate events such as the 5 December 2019 Ms 4.5 Fengnan event. It is still debated whether aftershock sequences following large earthquakes in low-seismicity continental regions can persist for several centuries. To understand the current stage of the Tangshan aftershock sequence, we analyze the sequence record and separate background seismicity from the triggering effect using a finite-source epidemic-type aftershock sequence model. Our results show that the background rate notably decreases after the mainshock. The estimated probability that the most recent 5 December 2019 Ms 4.5 Fengnan District, Tangshan, earthquake is a background event is 50.6%. This indicates that the contemporary seismicity in the Tangshan aftershock zone can be characterized as a transition from aftershock activity to background seismicity. Although the aftershock sequence is still active in the Tangshan region, it is overridden by background seismicity.

scholarly journals An algorithm for the assessment of several small rates

2012 ◽  
Vol 53 ◽  
Author(s):  
Leonidas Sakalauskas ◽  
Ingrida Vaičiulytė
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Approach ◽  
Maximum Likelihood Method ◽  
Rare Events ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Empirical Bayesian ◽  
Empirical Bayesian Approach

The present paper describes the empirical Bayesian approach applied in the estimation of several small rates. Modeling by empirical Bayesian approach the probabilities of several rare events, it is assumed that the frequencies of events follow to Poisson’s law with different parameters, which are correlated Gaussian random values. The unknown parameters are estimated by the maximum likelihood method computing the integrals appeared here by Hermite–Gauss quadratures. The equations derived that are satisfied by maximum likelihood estimates of model parameters.

scholarly journals Inverse Lomax-Exponentiated G (IL-EG) Family of Distributions: Properties and Applications

2020 ◽  
pp. 48-64
Author(s):  
Jamilu Yunusa Falgore ◽  
Sani Ibrahim Doguwa
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Baseline Model ◽  
New Family ◽  
Family Of Distributions ◽  
Better Than

A new generator of continuous distributions called the Inverse Lomax-Exponentiated G family, which has three extra positive parameters is proposed. The structural properties of the new family that holds for any continuous baseline model including explicit density function expressions, moments, inequality measurements, moment generating function, reliability functions, Renyi and Shanon entropies, and distribution of order statistics are derived. A Monte Carlo simulation to test the efficiency of the maximum likelihood estimates is conducted. The application of the new sub-model to the two data sets using the maximum likelihood method indicates that the new model is better than the existing competitors.

scholarly journals A study of aftershocks of 20 October 1991 Uttarkashi earthquake

MAUSAM ◽  
2022 ◽  
Vol 46 (4) ◽  
pp. 435-444
Author(s):  
R S. DATTATRAYAM ◽  
V.P. KAMBLE
Keyword(s):  
Decay Constant ◽  
Source Parameters ◽  
Temporal Distribution ◽  
B Value ◽  
Aftershock Sequence ◽  
Himalayan Region ◽  
Aftershock Activity ◽  
Field Surveys ◽  
Macroseismic Observations ◽  
Good Agreement

The Uttarkashi earthquake of 20 October 1991, which caused widespread damage in the Galhwal Himalayan region, was followed by a prominent aftershock. activity extending over a period of about two months. The aftershock activity was monitored using temporary networks established after the mainshock and the permanent stations in operation in the region. About 142 aftershocks could be located accurately using the data of these stations. The b-value of the Gutenberg-Richter's relationship for the aftershock sequence works out to be 0.6. The temporal distribution of the aftershocks suggests a hyperbolic decay with a decay constant (p) of 1.17. Macroseismic observations derived from field surveys show good agreement with the instrumentally determined source parameters.  

scholarly journals A Novel Generalized Family of Distributions for Engineering and Life Sciences Data Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Najma Salahuddin ◽  
Alamgir Khalil ◽  
Wali Khan Mashwani ◽  
Habib Shah ◽  
Pijitra Jomsri ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Mean Squared Error ◽  
Residual Life ◽  
Parametric Estimation ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Mean Residual Life ◽  
Estimation Of Parameters ◽  
Lifetime Distributions ◽  
The Family

In this paper, a new method is proposed to expand the family of lifetime distributions. The suggested method is named as Khalil new generalized family (KNGF) of distributions. A special submodel, termed as Khalil new generalized Pareto (KNGP) distribution, is investigated from the family with one shape and two scale parameters. A number of mathematical properties of the submodel have been derived including moments, moment-generating function, quantile function, entropy measures, order statistics, mean residual life function, and maximum likelihood method for the estimation of parameters. The proposed distribution is very flexible in its nature covering several hazard rate shapes (symmetric and asymmetric). To examine the performance of the maximum likelihood estimates in terms of their bias and mean squared error using simulated samples, a simulation study is carried out. Furthermore, parametric estimation of the model is conferred using the method of maximum likelihood, and the practicality of the proposed family is illustrated with the help of real datasets. Finally, we hope that the new suggested flexible KNGF may produce useful models for fitting monotonic and nonmonotonic data related to survival analysis and reliability analysis.

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