139,303 research outputs found
Distribution of Maximum Earthquake Magnitudes in Future Time Intervals, Application to the Seismicity of Japan (1923-2007)
We modify the new method for the statistical estimation of the tail
distribution of earthquake seismic moments introduced by Pisarenko et al.
[2009] and apply it to the earthquake catalog of Japan (1923-2007). The method
is based on the two main limit theorems of the theory of extreme values and on
the derived duality between the Generalized Pareto Distribution (GPD) and
Generalized Extreme Value distribution (GEV). We obtain the distribution of
maximum earthquake magnitudes in future time intervals of arbitrary duration
tau. This distribution can be characterized by its quantile Qq(tau) at any
desirable statistical level q. The quantile Qq(tau) provides a much more stable
and robust characteristic than the traditional absolute maximum magnitude Mmax
(Mmax can be obtained as the limit of Qq(tau) as q tends to 1, and tau tends to
infinity). The best estimates of the parameters governing the distribution of
Qq(tay) for Japan (1923-2007) are the following: Form parameter for GEV =
-0.1901 +- 0.0717; position parameter GEV(tau=200)= 6.3387 +- 0.0380; spread
parameter for GEV(tau=200)= 0.5995 +- 0.0223; Q_0.90,GEV(tau=10)= 8.34 +- 0.32.
We also estimate Qq(tau) for a set of q-values and future time periods in the
range for tau between 1 and 50 years from 2007. For comparison, the absolute
maximum estimate Mmax from GEV, which is equal to 9.57 +- 0.86, has a scatter
more than twice that of the 90 percent quantile Q_{0.90,GEV}(tau=10) of the
maximum magnitude over the next 10 years counted from 2007.Comment: 15 pages + 10 figure
Bootstrap predictive inference for ARIMA processes
In this study, we propose a new bootstrap strategy to obtain prediction intervals for autoregressive integrated moving-average processes. Its main advantage over other bootstrap methods previously proposed for autoregressive integrated processes is that variability due to parameter estimation can be incorporated into prediction intervals without requiring the backward representation of the process. Consequently, the procedure is very flexible and can be extended to processes even if their backward representation is not available. Furthermore, its implementation is very simple. The asymptotic properties of the bootstrap prediction densities are obtained. Extensive finite-sample Monte Carlo experiments are carried out to compare the performance of the proposed strategy vs. alternative procedures. The behaviour of our proposal equals or outperforms the alternatives in most of the cases. Furthermore, our bootstrap strategy is also applied for the first time to obtain the prediction density of processes with moving-average components.Publicad
The Overlooked Potential of Generalized Linear Models in Astronomy-III: Bayesian Negative Binomial Regression and Globular Cluster Populations
In this paper, the third in a series illustrating the power of generalized
linear models (GLMs) for the astronomical community, we elucidate the potential
of the class of GLMs which handles count data. The size of a galaxy's globular
cluster population is a prolonged puzzle in the astronomical
literature. It falls in the category of count data analysis, yet it is usually
modelled as if it were a continuous response variable. We have developed a
Bayesian negative binomial regression model to study the connection between
and the following galaxy properties: central black hole mass,
dynamical bulge mass, bulge velocity dispersion, and absolute visual magnitude.
The methodology introduced herein naturally accounts for heteroscedasticity,
intrinsic scatter, errors in measurements in both axes (either discrete or
continuous), and allows modelling the population of globular clusters on their
natural scale as a non-negative integer variable. Prediction intervals of 99%
around the trend for expected comfortably envelope the data,
notably including the Milky Way, which has hitherto been considered a
problematic outlier. Finally, we demonstrate how random intercept models can
incorporate information of each particular galaxy morphological type. Bayesian
variable selection methodology allows for automatically identifying galaxy
types with different productions of GCs, suggesting that on average S0 galaxies
have a GC population 35% smaller than other types with similar brightness.Comment: 14 pages, 12 figures. Accepted for publication in MNRA
Prediction of remaining life of power transformers based on left truncated and right censored lifetime data
Prediction of the remaining life of high-voltage power transformers is an
important issue for energy companies because of the need for planning
maintenance and capital expenditures. Lifetime data for such transformers are
complicated because transformer lifetimes can extend over many decades and
transformer designs and manufacturing practices have evolved. We were asked to
develop statistically-based predictions for the lifetimes of an energy
company's fleet of high-voltage transmission and distribution transformers. The
company's data records begin in 1980, providing information on installation and
failure dates of transformers. Although the dataset contains many units that
were installed before 1980, there is no information about units that were
installed and failed before 1980. Thus, the data are left truncated and right
censored. We use a parametric lifetime model to describe the lifetime
distribution of individual transformers. We develop a statistical procedure,
based on age-adjusted life distributions, for computing a prediction interval
for remaining life for individual transformers now in service. We then extend
these ideas to provide predictions and prediction intervals for the cumulative
number of failures, over a range of time, for the overall fleet of
transformers.Comment: Published in at http://dx.doi.org/10.1214/00-AOAS231 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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