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Related Concept Videos

Stratified Sampling Method01:16

Stratified Sampling Method

Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a stratified sample, divide the population into groups called strata and then take a...
Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
Sampling Distribution01:12

Sampling Distribution

Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
Sampling Methods: Overview01:06

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of sampling...
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...
Sampling Plans01:23

Sampling Plans

Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...

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Related Experiment Video

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Measuring Spatially- and Directionally-varying Light Scattering from Biological Material
11:57

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Published on: May 20, 2013

How old is this bird? The age distribution under some phase sampling schemes.

Sophie Hautphenne1,2, Melanie Massaro3, Peter Taylor4

  • 1School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC, 3010, Australia. sophiemh@unimelb.edu.au.

Journal of Mathematical Biology
|April 5, 2017
PubMed
Summary

This study models lifetime using Markov chains, finding that conditional age distributions depend on phase observation. These findings aid in computing age pyramids for endangered species like the Chatham Island black robin.

Keywords:
Age distributionPetroica traversiPhase-type distributionTransient Markov chain

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Area of Science:

  • Mathematical modeling
  • Population dynamics
  • Ecology

Background:

  • Individual lifetime can be modeled using finite-state continuous-time Markov chains.
  • The time of death follows a phase-type distribution, with transient states termed phases.

Purpose of the Study:

  • To determine the conditional age distribution of an individual given its current phase.
  • To investigate how different phase observation schemes affect this distribution.
  • To apply these findings to ecological studies, specifically age pyramid computation for the Chatham Island black robin.

Main Methods:

  • Utilized a finite-state continuous-time Markov chain model with one absorbing state.
  • Analyzed the conditional age distribution based on different phase observation schemes.
  • Applied the derived methods to calculate the age pyramid for Petroica traversi.

Main Results:

  • The conditional age distribution is dependent on the interpretation of the question and the specific phase observation scheme.
  • Successfully computed the age pyramid for the Chatham Island black robin population between 2007 and 2014.

Conclusions:

  • The phase-type distribution model provides a framework for understanding lifetime and age structure.
  • The study highlights the importance of defining observation schemes in Markov chain applications.
  • Results offer valuable insights for conservation efforts and population management of endangered species.