hypergeometric

简明释义

英[/ˌhaɪpərdʒiˈɔːmɛtrɪk/]美[/ˌhaɪpərdʒiˈɔːmɛtrɪk/]

adj. 超几何的

英英释义

单词用法

同义词

反义词

例句

1.In part II, we consider the recurrence formula of double hypergeometric terms.

在文章的第二部分，我们考虑了双超几何项的递推公式。

2.By the next morning I had established the existence of a class of Fuchsian functions, those which come from the hypergeometric series;

第二天早上之前，我已经建立好一类Fuchsian函数的存在性证明，这些函数来自于超几何序列；

3.The radial bound state solutions are expressed in terms of the confluent hypergeometric functions and the energy equation is derived from the boundary condition satisfied by the radial wavefunctions.

径向束缚态波函数用合流超几何函数表示，束缚态的能量方程可由径向波函数满足的边界条件得到。

4.This dissertation studies the applications of the inversion techniques and its equivalent form in finding and proving the hypergeometric series identities.

本文探讨了反演技术及其等价的形式在寻求和证明超几何级数恒等式方面的应用。

5.With the boundary conditions of bound states, we have obtained the corresponding energy spectrum via an expression and wave functions in terms of hypergeometric functions.

并利用束缚态边界条件，获得了束缚态能谱表达式和由超几何函数表示出的波函数。

6.In this paper, the inclination functions are expressed as the hypergeometric functions.

本文用超几何函数来表示倾角函数。

7.By using a simple algorithm for the summation of basic hypergeometric series, summation formulas for some basic hypergeometric series are obtained.

本文运用基本超几何级数求和的一个简单算法，求得一些基本超几何级数的求和公式。

8.In statistics, the hypergeometric 超几何分布 distribution is used to describe the probability of k successes in n draws without replacement.

在统计学中，hypergeometric 超几何分布 用于描述在不放回抽样的情况下，n次抽取中k次成功的概率。

9.The hypergeometric 超几何 test is often used to determine if there are more successes than expected in a sample.

常用的hypergeometric 超几何 检验用于确定样本中成功次数是否超过预期。

10.Researchers applied the hypergeometric 超几何 model to analyze the selection process in their experiment.

研究人员应用hypergeometric 超几何 模型分析了他们实验中的选择过程。

11.The hypergeometric 超几何 distribution is particularly useful in quality control scenarios.

在质量控制场景中，hypergeometric 超几何 分布特别有用。

12.Using the hypergeometric 超几何 probability formula, we can calculate the likelihood of drawing a certain number of red balls from a mixed bag.

使用hypergeometric 超几何 概率公式，我们可以计算从混合袋中抽取一定数量红球的可能性。

作文

In the realm of mathematics and statistics, the term hypergeometric refers to a specific type of distribution that is used to describe the probability of drawing successes in a sequence of draws without replacement from a finite population. This concept is particularly useful in scenarios where the population size is small and the sample size is a significant fraction of the population. The hypergeometric distribution is characterized by three parameters: the total number of items in the population, the number of successes in the population, and the number of draws made. Understanding this distribution can be crucial for researchers and statisticians when they are dealing with problems that involve sampling without replacement. To illustrate the importance of the hypergeometric distribution, let us consider a practical example. Imagine a box containing 10 balls, where 4 are red and 6 are blue. If we randomly draw 3 balls from the box, we might want to know the probability of drawing exactly 2 red balls. This scenario perfectly fits the framework of the hypergeometric distribution, as we are sampling without replacement from a finite population. The mathematical formula for calculating this probability involves combinations and can provide insightful information about the likelihood of various outcomes. The hypergeometric distribution stands in contrast to the binomial distribution, which assumes that draws are made with replacement. This distinction is vital, as the outcomes and probabilities can vary significantly between these two distributions. In situations where the sample size is large relative to the population, the binomial model may approximate the hypergeometric distribution, but it is essential to recognize the underlying assumptions of each model. Moreover, the applications of the hypergeometric distribution extend beyond simple probability calculations. It is frequently employed in fields such as genetics, quality control, and survey sampling. For instance, in genetics, researchers may use the hypergeometric model to determine the likelihood of inheriting a certain trait based on a limited number of samples from a larger population. In quality control, manufacturers may apply this distribution to assess the probability of finding defective items in a batch when inspecting a random sample. In conclusion, the concept of hypergeometric distribution is fundamental in the field of statistics, particularly when dealing with finite populations and sampling without replacement. Its relevance spans various disciplines, making it an essential tool for data analysis and interpretation. By understanding the principles behind the hypergeometric distribution, researchers and practitioners can make informed decisions based on probabilistic models that accurately reflect their sampling conditions. As we continue to explore the complexities of statistical methods, the hypergeometric distribution remains a powerful concept that enhances our ability to analyze and understand data effectively.

在数学和统计学领域，术语hypergeometric指的是一种特定类型的分布，用于描述从有限总体中不放回抽样时成功的概率。这个概念在总体规模较小且样本量占总体显著比例的情况下特别有用。hypergeometric分布的特点是三个参数：总体中的项目总数、总体中的成功数量和进行抽样的次数。理解这种分布对于研究人员和统计学家在处理涉及不放回抽样的问题时至关重要。 为了说明hypergeometric分布的重要性，让我们考虑一个实际的例子。想象一个盒子，里面有10个球，其中4个是红色的，6个是蓝色的。如果我们从盒子中随机抽取3个球，我们可能想知道抽到恰好2个红球的概率。这个场景完美契合了hypergeometric分布的框架，因为我们是在有限总体中不放回抽样。计算这个概率的数学公式涉及组合，可以提供关于各种结果可能性的深入信息。 hypergeometric分布与二项分布形成鲜明对比，后者假设抽样是放回的。这种区别至关重要，因为这两种分布之间的结果和概率可能会显著不同。在样本量相对于总体较大的情况下，二项模型可能会近似hypergeometric分布，但必须认识到每种模型的基本假设。 此外，hypergeometric分布的应用超越了简单的概率计算。它常被用于遗传学、质量控制和调查抽样等领域。例如，在遗传学中，研究人员可能使用hypergeometric模型来确定基于从更大群体中提取的有限样本继承某种性状的可能性。在质量控制中，制造商可能会应用这种分布来评估在随机样本中发现缺陷项目的概率。 总之，hypergeometric分布的概念在统计学领域是基础，尤其是在处理有限总体和不放回抽样时。它的相关性跨越多个学科，使其成为数据分析和解释的重要工具。通过理解hypergeometric分布背后的原理，研究人员和从业者可以根据准确反映其抽样条件的概率模型做出明智的决策。随着我们继续探索统计方法的复杂性，hypergeometric分布仍然是一个强大的概念，增强了我们有效分析和理解数据的能力。