Basic properties and parameter estimation of three parameter probability distributions of the Laplace and Cauchy type

2014 ◽  
Vol 2014 (2) ◽  
pp. 12-36
Author(s):  
Nikola Jaksic ◽  
Keyword(s):  
Parameter Estimation ◽  
Probability Distributions ◽  
Cauchy Type ◽  
Basic Properties

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

PURE AND O-SUBSTITUTION

2007 ◽  
Vol 18 (04) ◽  
pp. 829-845 ◽  
Author(s):  
ANDREAS MALETTI
Keyword(s):  
Probability Distributions ◽  
Basic Properties ◽  
Tree Series ◽  
Linear Probability

The basic properties of distributivity and deletion of pure and o-substitution are investigated. The obtained results are applied to show preservation of recognizability in a number of interesting cases. It is proved that linear and recognizable tree series are closed under o-substitution provided that the underlying semiring is commutative, continuous, and additively idempotent. It is known that, in general, pure substitution does not preserve recognizability (not even for linear target tree series), but it is shown that recognizable linear probability distributions (represented as tree series) are closed under pure substitution.

scholarly journals Probabilistic moveout analysis by time warping

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. U1-U20
Author(s):  
Yanadet Sripanich ◽  
Sergey Fomel ◽  
Jeannot Trampert ◽  
William Burnett ◽  
Thomas Hess
Keyword(s):  
Parameter Estimation ◽  
Posterior Probability ◽  
Model Building ◽  
Probability Distributions ◽  
Real Data ◽  
Inversion Method ◽  
Time Warping ◽  
Anisotropic Models ◽  
Trade Offs ◽  
Set Up

Parameter estimation from reflection moveout analysis represents one of the most fundamental problems in subsurface model building. We have developed an efficient moveout inversion method based on the process of automatic flattening of common-midpoint (CMP) gathers using local slopes. We find that as a by-product of this flattening process, we can also estimate reflection traveltimes corresponding to the flattened CMP gathers. This traveltime information allows us to construct a highly overdetermined system and subsequently invert for moveout parameters including normal-moveout velocities and quartic coefficients related to anisotropy. We use the 3D generalized moveout approximation (GMA), which can accurately capture the effects of complex anisotropy on reflection traveltimes as the basis for our moveout inversion. Due to the cheap forward traveltime computations by GMA, we use a Monte Carlo inversion scheme for improved handling of the nonlinearity between the reflection traveltimes and moveout parameters. This choice also allows us to set up a probabilistic inversion workflow within a Bayesian framework, in which we can obtain the posterior probability distributions that contain valuable statistical information on estimated parameters such as uncertainty and correlations. We use synthetic and real data examples including the data from the SEAM Phase II unconventional reservoir model to demonstrate the performance of our method and discuss insights into the problem of moveout inversion gained from analyzing the posterior probability distributions. Our results suggest that the solutions to the problem of traveltime-only moveout inversion from 2D CMP gathers are relatively well constrained by the data. However, parameter estimation from 3D CMP gathers associated with more moveout parameters and complex anisotropic models are generally nonunique, and there are trade-offs among inverted parameters, especially the quartic coefficients.

scholarly journals The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248873
Author(s):  
Majdah Badr ◽  
Muhammad Ijaz
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Probability Distribution ◽  
Simulation Study ◽  
Probability Distributions ◽  
Simulated Data ◽  
Maximum Likelihood Estimators ◽  
Data Sets ◽  
Lifetime Data ◽  
Confidence Bounds

The paper addresses a new four-parameter probability distribution called the Exponentiated Exponential Burr XII or abbreviated as EE-BXII. We derive various statistical properties in addition to the parameter estimation, moments, and asymptotic confidence bounds. We estimate the precision of the maximum likelihood estimators via a simulation study. Furthermore, the utility of the proposed distribution is evaluated by using two lifetime data sets and the results are compared with other existing probability distributions. The results clarify that the proposed distribution provides a better fit to these data sets as compared to the existing probability distributions.

scholarly journals Volatility dynamics and the risk-return relationship in South Africa: A GARCH approach

2021 ◽  
Vol 18 (2) ◽  
pp. 106-117
Author(s):  
Nitesha Dwarika ◽  
Peter Moores-Pitt ◽  
Retius Chifurira
Keyword(s):  
South Africa ◽  
Parameter Estimation ◽  
South African ◽  
Risk Estimation ◽  
Probability Distributions ◽  
Financial Data ◽  
Test Results ◽  
Sample Period ◽  
The South ◽  
Risk Return

This study is aimed at investigating the volatility dynamics and the risk-return relationship in the South African market, analyzing the FTSE/JSE All Share Index returns for an updated sample period of 2009–2019. The study employed several GARCH type models with different probability distributions governing the model’s innovations. Results have revealed strong persistent levels of volatility and a positive risk-return relationship in the South African market. Given the elaborate use of the GARCH approach of risk estimation in the existing finance literature, this study highlighted several weaknesses of the model. A noteworthy property of the GARCH approach was that the innovation distributions did not affect parameter estimation. Analyzing the GARCH type models, this theory was supported by the majority of the GARCH test results with respect to the volatility dynamics. On the contrary, it was strongly unsupported by the risk-return relationship. More specifically, it was found that while the innovations of the EGARCH (1, 1) model could account for the volatile nature of financial data, asymmetry remained uncaptured. As a result, misestimating of risks occurred, which could lead to inaccurate results. This study highlighted the significance of the innovation distribution of choice and recommended the exploration of different nonnormal innovation distributions to aid with capturing the asymmetry.

LOCATION PARAMETER ESTIMATION OF A MULTISPECTRAL SAMPLE BY A MEDIAN OPERATION

1988 ◽  
Vol 02 (02) ◽  
pp. 287-299 ◽  
Author(s):  
CARLOS A. POMALAZA-RÁEZ ◽  
YU-SHAN FONG
Keyword(s):  
Parameter Estimation ◽  
Probability Distributions ◽  
Location Parameter ◽  
Numerical Results ◽  
The Other ◽  
Statistical Characteristics ◽  
Simple Extension ◽  
Overall Performance ◽  
Numerical Complexity ◽  
Better Than

Three different kinds of median type estimators for use in applications where the underlying probability distributions are multivariate are proposed and analyzed. The numerical complexity and the statistical characteristics of the estimators are studied and discussed. Numerical results give evidence that the estimator which is a simple extension of the scalar median has an overall performance that is the same or better than the other two proposed estimators.

scholarly journals Comparing Estimation Methods for the FPLD

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Agostino Tarsitano
Keyword(s):  
Parameter Estimation ◽  
Statistical Models ◽  
Probability Distributions ◽  
Quantile Function ◽  
Alternative Methods ◽  
Estimation Methods ◽  
Random Numbers ◽  
Generalized Lambda Distribution ◽  
Proposed Model

We use the quantile function to define statistical models. In particular, we present a five-parameter version of the generalized lambda distribution (FPLD). Three alternative methods for estimating its parameters are proposed and their properties are investigated and compared by making use of real and simulated datasets. It will be shown that the proposed model realistically approximates a number of families of probability distributions, has feasible methods for its parameter estimation, and offers an easier way to generate random numbers.

A SURVEY ON DISCRETE LIFETIME DISTRIBUTIONS

2003 ◽  
Vol 10 (01) ◽  
pp. 69-98 ◽  
Author(s):  
CYRIL BRACQUEMOND ◽  
OLIVIER GAUDOIN
Keyword(s):  
Probability Distributions ◽  
Lifetime Distributions ◽  
Discrete Probability ◽  
Basic Properties ◽  
Comprehensive Survey ◽  
Polya Urn ◽  
Urn Scheme ◽  
Nonrepairable Systems ◽  
Discrete Probability Distributions

This paper presents a comprehensive survey of discrete probability distributions used in reliability for modeling discrete lifetimes of nonrepairable systems. The basic properties of each model are given. A classification into two families is proposed, highlighting the interest of using a Pólya urn scheme. The quality of the estimation of models parameters is numerically assessed. Some criteria are given in order to select among the presented distributions the most useful for applications.

Sign in / Sign up

Export Citation Format

Share Document