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Saying that a distribution is asymptotic means that as the sample size increases, the distribution of a statistic (such as the sample mean) approaches a specific limiting distribution, regardless of the original distribution of the data. This concept is often associated with the Central Limit Theorem, which states that the sampling distribution of the mean will tend to be normally distributed as the sample size becomes large. In practical terms, it implies that for large samples, the characteristics of the distribution can be effectively approximated, facilitating statistical inference.
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Is it possible for a function that has a horizontal asymptote to attain the value of an asymptote?
Yes. Think of a function that starts at the origin, increases rapidly at first and then decays gradually to an asymptotic value of 0. It will have attained its asymptotic value at the start. For example, the Fisher F distribution, which is often used, in statistics, to test the significance of regression coefficients. Follow the link for more on the F distribution.
What does it mean when you say a variable is normally distributed?
It means that the probability distribution function of the variable is the Gaussian or normal distribution.
How do the width and height of a normal distribution curve?
By standard practice, the normal distribution curve should be normalized so that the area under the curve is 1. This results in a height, at the mean, of about 0.4, i.e. the probability of a sample value being equal to the mean is 40 percent. The width of the normal distribution curve is infinite, as the tails are asymptotic to the X axis. It is easier to understand that the +/- one sigma area is 68.2 percent, the +/- two sigma area is 95.4 percent, and the +/- three sigma area is 99.6 percent.
In mathematics what is asymptotic analysis?
In mathematics, an asymptotic analysis is a method of describing limiting behaviour. The methodology has applications across science such as the analysis of algorithms.
How do you determine if a graph is asymptotic?
A graph of y against x has an asymptote if, its y value approaches some value k but never actually attains it. The value k is called its asymptotic value. These are often "infinities" when a denominator in the function approaches 0. For example, y = 1/(x-2) has an asymptotic value of minus infinity when x approaches 2 from below and an asymptotic value of + infinity from above. But the asymptotic value need not be infinite - they could be a "normal number. For example y = 3-x + 2.5 has an asymptotic value of 2.5. y is always greater than 2.5 and as x increases, it comes closer and closer to 2.5 but never actually attains that value.
What has the author John Edward Kolassa written?
John Edward Kolassa has written: 'Topics in series approximations to distribution functions' 'Series approximation methods in statistics' -- subject(s): Mathematical statistics, Asymptotic distribution (Probability theory), Edgeworth expansions, Asymptotic theory
Is it possible for a function that has a horizontal asymptote to attain the value of an asymptote?
Yes. Think of a function that starts at the origin, increases rapidly at first and then decays gradually to an asymptotic value of 0. It will have attained its asymptotic value at the start. For example, the Fisher F distribution, which is often used, in statistics, to test the significance of regression coefficients. Follow the link for more on the F distribution.
Why two tail of normal distribution do not touch the horizontal axis?
The domain of the Normal distribution is the whole of the real line. As a result the horizontal axis is asymptotic to the Normal distribution curve. The curve gets closer and closer to the axis but never, ever reaches it.
What has the author A W van der Vaart written?
A. W. van der Vaart has written: 'Asymptotic statistics' -- subject(s): Mathematical statistics, Asymptotic theory 'Weak convergence and empirical processes' -- subject(s): Stochastic processes, Convergence, Distribution (Probability theory), Sampling (Statistics)
What does it mean when you say a variable is normally distributed?
It means that the probability distribution function of the variable is the Gaussian or normal distribution.
What has the author Peter D Miller written?
Peter D. Miller has written: 'Applied asymptotic analysis' -- subject(s): Asymptotic theory, Differential equations, Integral equations, Approximation theory, Asymptotic expansions
How do the width and height of a normal distribution curve?
By standard practice, the normal distribution curve should be normalized so that the area under the curve is 1. This results in a height, at the mean, of about 0.4, i.e. the probability of a sample value being equal to the mean is 40 percent. The width of the normal distribution curve is infinite, as the tails are asymptotic to the X axis. It is easier to understand that the +/- one sigma area is 68.2 percent, the +/- two sigma area is 95.4 percent, and the +/- three sigma area is 99.6 percent.
What does it mean if the standard error is equal to the mean?
Nothing, really. You may be able to say more if you knew what the underlying distribution was.
What is conditional asymptotic notation?
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When you calculate mean is the answer same when the same data is calculated by median?
No. The mean and median are not necessarily the same. They will be the same if the distribution is symmetric but the converse is not necessarily true. That is to say, a distribution does not have to be symmetric for the mean and median to be the same. For example, the mean and median of {1, 1, 5, 6, 12} are both 5 but the distribution is NOT symmetric.
What has the author Edward Thomas Copson written?
Edward Thomas Copson has written: 'Asymptotic expansions' -- subject(s): Asymptotic expansions
Can lines of curvature be asymptotic curves?
A curve may be both asymptotic and a line of curvature, in which case the curve is a line (such as the rulings of a ruled surface).
