Percentile-based grain size distribution analysis tools (GSDtools) – estimating confidence limits and hypothesis tests for comparing two samples

Tests for an upper percentile of a lognormal distribution based on samples with multiple detection limits and sample-size calculation.

The problem of determining sample size for testing an upper percentile of a lognormal distribution based on samples with multiple detection limits is considered. Two tests, the signed likelihood ratio test and another test based on a pivotal statistic, are outlined. These tests are very satisfactory in controlling type I error rates and comparable in terms of powers. Procedures and R codes for ...

Confidence Intervals and Hypothesis Tests

Overview: Recall that a point estimator for a parameter of interest is a statistic which is a function of the random variables from which our sampling method chooses values. The properties of such an estimator, such as having a small bias or a small mean square error, are usually dependent only upon certain features of the sampling distribution of the statistic, such as its mean or variance. Ho...

Confidence limits for lognormal percentiles and for lognormal mean based on samples with multiple detection limits.

The problem of assessing occupational exposure using the mean or an upper percentile of a lognormal distribution is addressed. Inferential methods for constructing an upper confidence limit for an upper percentile of a lognormal distribution and for finding confidence intervals for a lognormal mean based on samples with multiple detection limits are proposed. The proposed methods are based on t...

Estimating the Saturated Hydraulic Conductivity of Granular Material, Using Artificial Neural Network, Based on Grain Size Distribution Curve

Confidence interval for the two-parameter exponentiated Gumbel distribution based on record values

In this paper, we study the estimation problems for the two-parameter exponentiated Gumbel distribution based on lower record values. An exact confidence interval and an exact joint confidence region for the parameters are constructed. A simulation study is conducted to study the performance of the proposed confidence interval and region. Finally, a numerical example with real data set is gi...