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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...
4.1K
Normal Distribution01:11

Normal Distribution

11.4K
The normal, a continuous distribution, is the most important of all the distributions. Its graph is a bell-shaped symmetrical curve, which is observed in almost all disciplines. Some of these include psychology, business, economics, the sciences, nursing, and, of course, mathematics. Some instructors may use the normal distribution to help determine students’ grades. Most IQ scores are normally distributed. Often real-estate prices fit a normal distribution. The normal distribution is...
11.4K
Confidence Intervals01:21

Confidence Intervals

6.5K
An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...
6.5K
Prediction Intervals01:03

Prediction Intervals

2.3K
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
2.3K
Choosing Between z and t Distribution01:25

Choosing Between z and t Distribution

2.8K
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...
2.8K
Student t Distribution01:31

Student t Distribution

6.1K
The population standard deviation is rarely known in many day-to-day examples of statistics. When the sample sizes are large, it is easy to estimate the population standard deviation using a confidence interval, which provides results close enough to the original value. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
The Student t distribution was developed by William S. Goset (1876–1937) of the...
6.1K

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相关实验视频

Updated: Jul 20, 2025

How to Create and Use Binocular Rivalry
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How to Create and Use Binocular Rivalry

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零调整后的日志对称分布:点和间隔估计.

Diego Risco-Cosavalente1, Francisco José A Cysneiros1

  • 1Universidade Federal de Pernambuco, Departamento de Estatística, Av. Prof Luiz Freire, s/n, Cidade Universitária, 50670-901 Recife, PE, Brazil.

Anais da Academia Brasileira de Ciencias
|August 2, 2023
PubMed
概括
此摘要是机器生成的。

对于半连续数据,引入了一个新的零调整日志对称分布. 这种灵活的模型使用最大概率进行估计,对具有不同数据尾巴的真实应用具有前景.

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科学领域:

  • 统计 统计 统计 统计
  • 可能性理论概率理论.
  • 数据分析 数据分析

背景情况:

  • 半连续数据在生物统计学和计量经济学等领域很常见,通常需要专门的建模方法.
  • 现有的分布可能无法充分捕捉具有高比例零值和连续正元件的数据的特征.

研究的目的:

  • 介绍和研究一个新型类型的半连续概率分布:零调整的逻辑对称 (ZALS) 分布.
  • 为了获得ZALS家族的关键性质和参数估计方法.
  • 通过模拟来评估拟议的估计器的性能,并通过真实数据证明其实际实用性.

主要方法:

  • ZALS分布属性的理论推导.
  • 应用最大概率估计 (MLE) 方法进行参数估计.
  • 对估计参数的信任区间 (CI) 的开发.
  • 进行模拟研究,以评估不同尾巴行为 (较轻/较重) 的MLE性能.
  • 使用现实世界数据集的示例应用.

主要成果:

  • 正式定义了ZALS分布,并确定了它的基本属性.
  • 对 ZALS 参数的最大概率估计和置信区间得到推导.
  • 模拟结果表明,MLEs在更轻的和更重的尾巴场景中都表现良好.
  • 实际数据应用证明了ZALS分布的实际适用性和灵活性.

结论:

  • 拟议的零调整日志对称分布为模拟半连续数据提供了灵活有效的工具.
  • 最大概率方法为这种新类分布提供了可靠的参数估计.
  • ZALS家族是分析复杂数据集的统计工具包中的一个有价值的补充,具有零膨胀和连续组件.