Bivariate normal distribution fitting on discontinuity orientation clusters

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

A bivariate normal density function has been used to represent discontinuity orientation cluster distributions. Goodness-of-fit tests should be performed in order to make decisions on the representation of discontinuity clusters by theoretical probability distributions. In the literature, graphical procedures are available to fit a bivariate normal distribution to discontinuity clusters. However, these procedures assume no correlation between the two orientation parameters. In this paper (a) a numerical procedure, and (b) a semigraphical procedure are given to perform a κ{script}2 goodness-of-fit test for bivariate normal distributions having nonzero correlation coefficient between the two parameters. These procedures were applied to a selected discontinuity cluster. The semigraphical procedure was found to be a time-consuming process. On the other hand, rapid computation can be done with the computer program developed for the numerical method. Sensitivity of the κ{script}2 test results of the IXJ grid setup was investigated. Mean orientation estimation for the cluster based on the equal area polar projection was compared with the estimation based on the moment estimate method. For the cluster analyzed, estimations of bivariate normal parameters {Mathematical expression} and {Mathematical expression}, based on the equal-area polar projection, and values based on the moment estimation method were found to be different up to about 6.7% of the values based on the moment estimation method.

Original languageEnglish (US)
Pages (from-to)181-195
Number of pages15
JournalMathematical Geology
Volume18
Issue number2
DOIs
StatePublished - Feb 1986

Fingerprint

Bivariate Normal Distribution
Discontinuity
discontinuity
estimation method
Moment Estimation
Bivariate Normal
Goodness of Fit Test
Projection
numerical method
Moment Estimate
Normal Function
Numerical Procedure
software
Density Function
Correlation coefficient
distribution
Two Parameters
Probability Distribution
Numerical Methods
Grid

Keywords

  • bivariate normal distribution
  • discontinuity orientation
  • goodness-of-fit test

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Earth and Planetary Sciences (miscellaneous)

Cite this

Bivariate normal distribution fitting on discontinuity orientation clusters. / Kulatilake, Pinnaduwa.

In: Mathematical Geology, Vol. 18, No. 2, 02.1986, p. 181-195.

Research output: Contribution to journalArticle

@article{3823ae20c4a4499eafd274b24aa94c07,
title = "Bivariate normal distribution fitting on discontinuity orientation clusters",
abstract = "A bivariate normal density function has been used to represent discontinuity orientation cluster distributions. Goodness-of-fit tests should be performed in order to make decisions on the representation of discontinuity clusters by theoretical probability distributions. In the literature, graphical procedures are available to fit a bivariate normal distribution to discontinuity clusters. However, these procedures assume no correlation between the two orientation parameters. In this paper (a) a numerical procedure, and (b) a semigraphical procedure are given to perform a κ{script}2 goodness-of-fit test for bivariate normal distributions having nonzero correlation coefficient between the two parameters. These procedures were applied to a selected discontinuity cluster. The semigraphical procedure was found to be a time-consuming process. On the other hand, rapid computation can be done with the computer program developed for the numerical method. Sensitivity of the κ{script}2 test results of the IXJ grid setup was investigated. Mean orientation estimation for the cluster based on the equal area polar projection was compared with the estimation based on the moment estimate method. For the cluster analyzed, estimations of bivariate normal parameters {Mathematical expression} and {Mathematical expression}, based on the equal-area polar projection, and values based on the moment estimation method were found to be different up to about 6.7{\%} of the values based on the moment estimation method.",
keywords = "bivariate normal distribution, discontinuity orientation, goodness-of-fit test",
author = "Pinnaduwa Kulatilake",
year = "1986",
month = "2",
doi = "10.1007/BF00898282",
language = "English (US)",
volume = "18",
pages = "181--195",
journal = "Mathematical Geosciences",
issn = "1874-8961",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - Bivariate normal distribution fitting on discontinuity orientation clusters

AU - Kulatilake, Pinnaduwa

PY - 1986/2

Y1 - 1986/2

N2 - A bivariate normal density function has been used to represent discontinuity orientation cluster distributions. Goodness-of-fit tests should be performed in order to make decisions on the representation of discontinuity clusters by theoretical probability distributions. In the literature, graphical procedures are available to fit a bivariate normal distribution to discontinuity clusters. However, these procedures assume no correlation between the two orientation parameters. In this paper (a) a numerical procedure, and (b) a semigraphical procedure are given to perform a κ{script}2 goodness-of-fit test for bivariate normal distributions having nonzero correlation coefficient between the two parameters. These procedures were applied to a selected discontinuity cluster. The semigraphical procedure was found to be a time-consuming process. On the other hand, rapid computation can be done with the computer program developed for the numerical method. Sensitivity of the κ{script}2 test results of the IXJ grid setup was investigated. Mean orientation estimation for the cluster based on the equal area polar projection was compared with the estimation based on the moment estimate method. For the cluster analyzed, estimations of bivariate normal parameters {Mathematical expression} and {Mathematical expression}, based on the equal-area polar projection, and values based on the moment estimation method were found to be different up to about 6.7% of the values based on the moment estimation method.

AB - A bivariate normal density function has been used to represent discontinuity orientation cluster distributions. Goodness-of-fit tests should be performed in order to make decisions on the representation of discontinuity clusters by theoretical probability distributions. In the literature, graphical procedures are available to fit a bivariate normal distribution to discontinuity clusters. However, these procedures assume no correlation between the two orientation parameters. In this paper (a) a numerical procedure, and (b) a semigraphical procedure are given to perform a κ{script}2 goodness-of-fit test for bivariate normal distributions having nonzero correlation coefficient between the two parameters. These procedures were applied to a selected discontinuity cluster. The semigraphical procedure was found to be a time-consuming process. On the other hand, rapid computation can be done with the computer program developed for the numerical method. Sensitivity of the κ{script}2 test results of the IXJ grid setup was investigated. Mean orientation estimation for the cluster based on the equal area polar projection was compared with the estimation based on the moment estimate method. For the cluster analyzed, estimations of bivariate normal parameters {Mathematical expression} and {Mathematical expression}, based on the equal-area polar projection, and values based on the moment estimation method were found to be different up to about 6.7% of the values based on the moment estimation method.

KW - bivariate normal distribution

KW - discontinuity orientation

KW - goodness-of-fit test

UR - http://www.scopus.com/inward/record.url?scp=34248199065&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34248199065&partnerID=8YFLogxK

U2 - 10.1007/BF00898282

DO - 10.1007/BF00898282

M3 - Article

AN - SCOPUS:34248199065

VL - 18

SP - 181

EP - 195

JO - Mathematical Geosciences

JF - Mathematical Geosciences

SN - 1874-8961

IS - 2

ER -