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Related Concept Videos

Confidence Coefficient01:24

Confidence Coefficient

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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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 confidence...
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Interpretation of Confidence Intervals01:19

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
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Uncertainty: Confidence Intervals00:54

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Applications of Integration to Probability Density Functions01:27

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Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF),...
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Estimating Population Mean with Unknown Standard Deviation01:22

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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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Recursive confidence band construction for an unknown distribution function.

Seksan Kiatsupaibul1, Anthony J Hayter

  • 1Department of Statistics Chulalongkorn University Bangkok, Thailand.

Biometrical Journal. Biometrische Zeitschrift
|May 28, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces novel recursive methods for constructing nonparametric confidence bands for distribution functions. These methods offer simultaneous statistical inferences on quantiles and cumulative probabilities, addressing multiplicity issues effectively.

Keywords:
Confidence bandsMultinomial distributionQuantilesRecursive methodologiesSimultaneous confidence intervals

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Area of Science:

  • Statistics
  • Statistical Inference
  • Nonparametric Statistics

Background:

  • Constructing confidence bands for distribution functions is fundamental in statistical inference.
  • Existing methods like Kolmogorov's procedure address multiplicity but can be extended.
  • Confidence bands offer simultaneous inferences on quantiles and cumulative probabilities.

Purpose of the Study:

  • To develop novel recursive methodologies for constructing one-sided and two-sided confidence bands.
  • To provide a fully nonparametric approach without assumptions on the distribution function.
  • To offer practical implementation with available R code.

Main Methods:

  • Utilizing recursive integration to bound cumulative probabilities at data points.
  • Employing recursive summations of multinomial probabilities to bound specified quantiles.
  • Developing both one-sided and two-sided confidence bands.

Main Results:

  • Demonstrated the efficacy of recursive methodologies for confidence band construction.
  • Provided two distinct recursive approaches for different inferential goals.
  • Illustrated the methods with practical examples.

Conclusions:

  • Recursive methodologies offer a powerful and flexible approach to nonparametric confidence band construction.
  • These methods effectively handle simultaneous inferences and multiplicity.
  • The developed techniques are practical and readily implementable using provided R code.