Related Experiment Video
Updated: Feb 13, 2026
09:42
Using SecM Arrest Sequence as a Tool to Isolate Ribosome Bound Polypeptides
Published on: June 19, 2012
12.8K
Exponential bounds for the hypergeometric distribution
1Department of Statistics, University of Washington, Seattle, WA 98195-4322, USA.
Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability
|March 10, 2018
Summary
This study provides exponential bounds for the hypergeometric distribution, incorporating a finite sampling correction. These bounds are comparable to those for the binomial distribution and extend existing convex ordering principles.
Area of Science:
- Probability theory
- Statistical analysis
Background:
- Existing bounds for binomial distribution by León and Perron, and Talagrand.
- Kemperman's convex ordering for sampling without replacement.
Purpose of the Study:
- Establish exponential bounds for the hypergeometric distribution.
- Incorporate a finite sampling correction factor.
- Extend Kemperman's convex ordering.
Main Methods:
- Derivation of exponential bounds.
- Application of convex ordering principles.
- Analysis of sampling without replacement.
Main Results:
- New exponential bounds for hypergeometric distribution established.
- Finite sampling correction factor included in bounds.
- Convex ordering extended to populations of real numbers (0, 1).
Conclusions:
- The derived bounds offer improved accuracy for hypergeometric probabilities.
- The extreme case of the extended convex ordering corresponds to a hypergeometric distribution.
- Findings contribute to a deeper understanding of sampling distributions.
Related Concept Videos
01:30Exponential Functions with Base e
264
Exponential functions with base e are essential for modeling continuous processes of growth and decay. The constant e, approximately 2.718, naturally arises in systems where change occurs proportionally to the current value. A positive exponent represents continuous growth, while a negative exponent represents continuous decay. These functions are especially useful for describing situations where change happens smoothly over time rather than in discrete steps.One clear example of exponential...
264
01:18Exponential and Sinusoidal Signals
759
The exponential function is crucial for characterizing waveforms that rise and decay rapidly. This continuous-time exponential function is defined using exponential terms with constants α and A. When both constants are real, the function is represented as,
759
01:29Exponential Growth
71
Bacterial populations exhibit exponential growth when conditions such as nutrient availability and temperature are favorable. In this phase, cells reproduce through binary fission, where each cell divides into two identical daughter cells. This process causes the population to double at regular intervals, resulting in a growth rate that is directly proportional to the current number of cells. As the population increases, the number of new cells formed during each generation also grows, creating...
71
01:29Introduction to Exponential Functions
431
Exponential functions are fundamental in modeling dynamic processes where the rate of change is proportional to the current value. Defined by f(x) = bx, where b is a positive constant not equal to one, they form the basis for describing processes of growth and decay depending on whether the base b is greater than or less than one.Exponential models describe situations where change occurs at a rate proportional to the current amount. These include phenomena such as bacterial proliferation,...
431
01:24Exponential Fourier series
778
In audio signal processing, the exponential Fourier series plays a crucial role in sound synthesis, allowing complex sounds to be broken down into simpler sinusoidal components. This decomposition process is fundamental in analyzing and reconstructing musical notes and other audio signals. The exponential Fourier series expresses periodic signals as the sum of complex exponentials at both positive and negative harmonic frequencies, providing a powerful tool for signal analysis.
Euler's identity...
Euler's identity...
778
02:33Exponential Equations for Modeling Growth
265
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
265