Welcome to the Hammerling Research Group's right-skewed sampling webtool!

This webtool is based on a paper by Dr. William Daniels and Dr. Dorit Hammerling that discusses the statistical implications of sampling from right-skewed distributions, such as the distributions of methane emissions from the oil and gas sector. To obtain an accurate inventory of emissions, it is essential to provide a large enough sample so that estimated average emissions closely approximate true average emissions.


This tool allows you to reproduce some of the results from the paper for a distribution of your choice. The results you will see include:

Density Plot

Density plot of your emission rate distribution and a rug plot that shows all rates and provides a clear visualization of the scale of the largest rates.

Interactive Figure: Sample Means by Size

Distributions of sample means at different sample sizes. You can click on this plot to see a histogram of the distribution and some summary metrics at a given sample size. You can also see line plots of additional error metrics.

Summary Table

Summary metrics for the sample mean at different sample sizes.


The tool has three sections where you can view and customize results:

Paper Distributions

In this tab, you can obtain results from distributions analyzed in the paper, which are emission rate distributions created by Williams et al. and Sherwin et al.

Parametric

In this tab, you can obtain results for one of the following four distributions: Lognormal, Weibull, Pareto, and Inverse Gaussian. For the distribution you choose, you can specify the parameters.

Upload

In this tab, you can upload your own CSV file with an emission rate distribution and obtain results.


Note: distribution sizes do not necessarily represent the number of sites in the selected basin.
Click on the heatmap to the left to see a histogram of percent differences at a certain sample size along with the mean and median percent difference. The pink line shows where you clicked.


Note: we treat 10,000 samples from the theoretical distribution as the true distribution.
Click on the heatmap to the left to see a histogram of percent differences at a certain sample size along with the mean and median percent difference. The pink line shows where you clicked.

Note: the CSV file you upload should have samples from your emission rate distribution in the first column (there should not be a column of row names). The column's name can be anything.

Note: if your distribution has over 10,000 rates in it, to avoid unreasonably long computation times we sample 10,000 rates from it and treat this sample as the true distribution.
Click on the heatmap to the left to see a histogram of percent differences at a certain sample size along with the mean and median percent difference. The pink line shows where you clicked.

Michael Basanese

Graduate Student | Research Assistant


I am a graduate student in statistics at the Colorado School of Mines and a research assistant in the Hammerling Research Group. I developed this app for my research group to help us provide targeted sample size guidance for methane measurement campaigns in the oil and gas sector. If you have any questions about this app or would like to make a suggestion, feel free to send me an email at mbasanese@mines.edu.