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関連する概念動画

Stratified Sampling Method01:16

Stratified Sampling Method

14.4K
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...
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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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What are Estimates?01:06

What are Estimates?

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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such...
7.9K
Sampling Plans01:23

Sampling Plans

855
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...
855
Quartile01:15

Quartile

8.6K
Quartiles are numbers that separate the data into quarters. Quartiles may or may not be part of the data. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data. To get the idea, consider the same data set:
1; 1; 2; 2; 4; 6; 6.8; 7.2; 8; 8.3; 9; 10; 10; 11.5
The median or second quartile is seven. The lower half of the...
8.6K
Choosing Between z and t Distribution01:25

Choosing Between z and t Distribution

3.5K
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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関連する実験動画

Updated: Jan 7, 2026

Sampling Soils in a Heterogeneous Research Plot
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中央値推定における分位数変換の応用：層化二相サンプリング

Fatimah A Almulhim1, Hassan M Aljohani2

  • 1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.

Entropy (Basel, Switzerland)
|December 24, 2025
PubMed
まとめ
この要約は機械生成です。

新しい分位数ベースの中央値推定法は、層化サンプリングにおける精度と頑健性を向上させます。これらの手法は、特に歪んだデータにおいて、実用的な中央値推定のための精度と有効性を高めます。

キーワード:
モンテカルロシミュレーション補助情報バイアス平均二乗誤差中央値推定分位数変換相対効率層化二相サンプリング

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関連する実験動画

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Inverse Probability of Treatment Weighting Propensity Score using the Military Health System Data Repository and National Death Index
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科学分野:

  • 統計学
  • 調査方法論

背景:

  • 従来の中央値推定法は、正規性を仮定することが多く、外れ値の影響を受けやすいです。
  • この感度は、正規分布でない、または歪んだデータを用いた実世界のアプリケーションにおける信頼性を制限します。

研究 の 目的:

  • 新しい分位数ベースの中央値推定法を導入すること。
  • 層化二相サンプリングにおける精度と頑健性を向上させること。
  • 補助データを使用して中央値推定の効率を改善すること。

主な方法:

  • 層化二相サンプリングの枠組み内で変換手法を利用しました。
  • 分位数ベースの中央値推定法を開発しました。
  • 一次近似を通じてバイアスおよび平均二乗誤差（MSE）の式を導出しました。
  • MSEを使用して推定量の効率を評価しました。

主要な成果:

  • 提案された推定法は、歪んだ分布下でのシミュレーションにおいて優れた性能を示しました。
  • 実在の母集団データセットに対する分析により、新しい手法の有効性が確認されました。
  • 分位数ベースの推定法は、既存のアプローチと比較して、より高い精度と有効性を達成しました。

結論:

  • 新しい分位数ベースの中央値推定法は、実用的なアプリケーションにおいて頑健かつ正確です。
  • これらの推定法は、中央値推定のためのより効果的な代替手段を提供し、特に層化サンプリングのシナリオにおいて有用です。
  • これらの手法は、補助データの有用性を高め、異質な層でも良好に機能します。