*Andy Hector*

- Published in print:
- 2015
- Published Online:
- March 2015
- ISBN:
- 9780198729051
- eISBN:
- 9780191795855
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198729051.003.0008
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Ecology

This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to ...
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This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to achieve this. A linear regression of transformed data is compared with the generalized linear model equivalent that avoids transformation by using a link function and non-normal distributions. Generalized linear models based on maximum likelihood use a link function to model the mean (in this case a square-root link) and a variance function to model the variability (in this case the gamma distribution where the variance increases as the square of the mean). The Box–Cox family of transformations is explained in detail.Less

This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to achieve this. A linear regression of transformed data is compared with the generalized linear model equivalent that avoids transformation by using a link function and non-normal distributions. Generalized linear models based on maximum likelihood use a link function to model the mean (in this case a square-root link) and a variance function to model the variability (in this case the gamma distribution where the variance increases as the square of the mean). The Box–Cox family of transformations is explained in detail.

*P.J. Lee*

*Jo Anne DeGraffenreid (ed.)*

- Published in print:
- 2008
- Published Online:
- November 2020
- ISBN:
- 9780195331905
- eISBN:
- 9780197562550
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195331905.003.0010
- Subject:
- Earth Sciences and Geography, Geophysics: Earth Sciences

In Chapter 3 we discussed the concepts, functions, and applications of the two discovery process models LDSCV and NDSCV. In this chapter we will use various simulated ...
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In Chapter 3 we discussed the concepts, functions, and applications of the two discovery process models LDSCV and NDSCV. In this chapter we will use various simulated populations to validate these two models to examine whether their performance meets our expectations. In addition, lognormal assumptions are applied to Weibull and Pareto populations to assess the impact on petroleum evaluation as a result of incorrect specification of probability distributions. A mixed population of two lognormal populations and a mixed population of lognormal, Weibull, and Pareto populations were generated to test the impact of mixed populations on assessment quality. NDSCV was then applied to all these data sets to validate the performance of the models. Finally, justifications for choosing a lognormal distribution in petroleum assessments are discussed in detail. Known populations were created as follows: A finite population was generated from a random sample of size 300 (N = 300) drawn from the lognormal, Pareto, and Weibull superpopulations. For the lognormal case, a population with μ = 0 and σ2 = 5 was assumed. The truncated and shifted Pareto population with shape factor θ = 0.4, maximum pool size = 4000, and minimum pool size = 1 was created. The Weibull population with λ = 20, θ = 1.0 was generated for the current study. The first mixed population was created by mixing two lognormal populations. Parameters for population I are μ = 0, σ2 = 3, and N1 = 150. For population II, μ = 3.0, σ2 = 3.2, and N2 = 150. The second mixed population was generated by mixing lognormal (N1 = 100), Pareto (N2 = 100), and Weibull (N3 = 100) populations with a total of 300 pools. In addition, a gamma distribution was also used for reference. The lognormal distribution is J-shaped if an arithmetic scale is used for the horizontal axis, but it shows an almost symmetrical pattern when a logarithmic scale is applied.
Less

In Chapter 3 we discussed the concepts, functions, and applications of the two discovery process models LDSCV and NDSCV. In this chapter we will use various simulated populations to validate these two models to examine whether their performance meets our expectations. In addition, lognormal assumptions are applied to Weibull and Pareto populations to assess the impact on petroleum evaluation as a result of incorrect specification of probability distributions. A mixed population of two lognormal populations and a mixed population of lognormal, Weibull, and Pareto populations were generated to test the impact of mixed populations on assessment quality. NDSCV was then applied to all these data sets to validate the performance of the models. Finally, justifications for choosing a lognormal distribution in petroleum assessments are discussed in detail. Known populations were created as follows: A finite population was generated from a random sample of size 300 (N = 300) drawn from the lognormal, Pareto, and Weibull superpopulations. For the lognormal case, a population with μ = 0 and σ2 = 5 was assumed. The truncated and shifted Pareto population with shape factor θ = 0.4, maximum pool size = 4000, and minimum pool size = 1 was created. The Weibull population with λ = 20, θ = 1.0 was generated for the current study. The first mixed population was created by mixing two lognormal populations. Parameters for population I are μ = 0, σ2 = 3, and N1 = 150. For population II, μ = 3.0, σ2 = 3.2, and N2 = 150. The second mixed population was generated by mixing lognormal (N1 = 100), Pareto (N2 = 100), and Weibull (N3 = 100) populations with a total of 300 pools. In addition, a gamma distribution was also used for reference. The lognormal distribution is J-shaped if an arithmetic scale is used for the horizontal axis, but it shows an almost symmetrical pattern when a logarithmic scale is applied.