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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
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Choosing Between z and t Distribution01:25

Choosing Between z and t Distribution

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The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to use for a calculation, one needs to determine the sample size, the nature of the distribution, and whether the population standard deviation is known. If the population standard deviation is known and the population is normally distributed, or if the sample size is greater than 30, the z distribution is preferred. The Student t distribution is...
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Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Related Experiment Video

Updated: Aug 26, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Bayesian variable selection in quantile regression with random effects: an application to Municipal Human Development

Marcus G L Nascimento1, Kelly C M Gonçalves1

  • 1Departamento de Métodos Estatísticos, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil.

Journal of Applied Statistics
|October 10, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new Bayesian method for analyzing income inequality, focusing on the Municipal Human Development Index (MHDI-I). The approach uses quantile regression to better understand factors influencing living standards across different income levels.

Keywords:
Location-scale mixture representationMCMC algorithmhierarchical models

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Area of Science:

  • Socioeconomic indicators
  • Statistical modeling
  • Bayesian econometrics

Background:

  • The Municipal Human Development Index - Income (MHDI-I) reflects a municipality's capacity to meet basic needs.
  • Understanding socioeconomic drivers of MHDI-I is crucial for public policy.
  • Income inequality necessitates analysis beyond simple averages, focusing on quantiles.

Purpose of the Study:

  • To develop a Bayesian variable selection method for quantile regression models.
  • To incorporate hierarchical random effects for robust analysis.
  • To identify key socioeconomic variables associated with MHDI-I across income distribution.

Main Methods:

  • Bayesian variable selection using spike-and-slab priors.
  • Quantile regression with a Generalized Asymmetric Laplace likelihood.
  • Hierarchical random effects models.

Main Results:

  • The proposed Bayesian method effectively performs variable selection in quantile regression.
  • The Generalized Asymmetric Laplace distribution offers a flexible alternative for modeling income data.
  • Application to Rio de Janeiro's MHDI-I demonstrates the method's practical utility.

Conclusions:

  • The developed Bayesian approach provides a powerful tool for analyzing income disparities.
  • This method enhances understanding of factors influencing living standards at various income quantiles.
  • The findings can inform targeted public policies for socioeconomic development.