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How do you model a weibull distribution using mean and variance?
Major step is to set the Weibull shape parameter at 3.6 to approximate the Normal.
What are characteristics of the X2?
It is not negative. it is positively skewed, and it approaches a normal distribution as the degrees of freedom increase. Its shape is NEVER based on the sample size.
What describes the shape of a distribution which is approximately normal?
A "bell" shape.
What is the approximate eccentricity of the shape to the right?
~ 42
What is the shape of a z-score distribution?
The standard normal distribution or the Gaussian distribution with mean 0 and variance 1.
What is the expected shape of the distribution of the sample mean?
The distribution of the sample mean is bell-shaped or is a normal distribution.
What does the Central Limit Theorem say about the traditional sample size that separates a large sample size from a small sample size?
The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.
What is the shape of the distribution of the mean of a sample?
The mean of a sample is a single value and so its distribution is a single value with probability 1.
What is the sampling distribution of sample means and why is it useful?
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
How many observations to assume a Normal distribution?
32 if you sample is a random sample. Other methods look at the shape of the data and how skewed it is.
How is frequency distribution useful to us?
I suspect you are referring to a sample frequency distribution.Providing that the sample size is sufficiently large there are various kinds of information that can be gleaned from one:the approximate range of values in the populationthe location of the population as measured by the value that appears most often in the frequency distribution-known as its modethe likely shape of the population's distribution, in particular whether it is symmetric or skewedobviously how values of the population variable are distributedwhether there are any curious peaks or valleys, even when the sample size is largethe amount of variation around the central value
How does the number of repetitions effect the shape of the normal distribution?
When we discuss a sample drawn from a population, the larger the sample, or the large the number of repetitions of the event, the more certain we are of the mean value. So, when the normal distribution is considered the sampling distribution of the mean, then more repetitions lead to smaller values of the variance of the distribution.
What does a negative kurtosis mean?
It means distribution is flater then [than] a normal distribution and if kurtosis is positive[,] then it means that distribution is sharper then [than] a normal distribution. Normal (bell shape) distribution has zero kurtosis.
The histogram of a sample should have a distribution shape that is skewed. Is this true or false?
False. It can be skewed to the left or right or be symmetrical.
What is the mean of the sampling distribution of the sample mean?
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
How do you model a weibull distribution using mean and variance?
Major step is to set the Weibull shape parameter at 3.6 to approximate the Normal.
When the sample size is large valid confidence intervals can be established for the population mean irrespective of the shape of the underlying distribution?
Yes, but that begs the question: how large should the sample size be?
