What is the minimum sample size to generate a Weibull distribution?
What is the minimum sample size to generate a Weibull distribution?
(OP)
One of the advantages of the Weibull is you can form a distribution with a much smaller sample size than say a histogram.
I experimented with using only the first 5 data points from a sample set of 26 to do a Weibull analysis. The first 5 points fit a 2 parameter Weibull and gave an R^2 values of 0.99. The second data set (remaining 21 points) changes to a 3 parameter Weibull with an R^2 value somewhere in the neighborhood of 0.976. So my questions are
1) What is the minimum sample size you need to accurately represent the population? For example from this sample size X the PDF is within some metric (std deviations, % etc) of the true PDF. Clearly R^2 value alone isn’t a good metric
2) I would like to plot the remaining 21 data points over the CDF calculated from my first 5 points. I have used 2 methods. Simply calculating the MR and plotting test cycle vs MR. The second using the Beta and Eta to calculate the CDF percent and plotting test cycle vs CDF percentile. Is there a good way to represent predicted CDF vs test data?
Here is my data set.
154173
171158
83431
201778
117578
192083
136262
149487
148009
98317
69798
94195
62548
103574
108364
132377
143047
85272
95760
214166
289237
161265
172490
99972
117440
89717
I experimented with using only the first 5 data points from a sample set of 26 to do a Weibull analysis. The first 5 points fit a 2 parameter Weibull and gave an R^2 values of 0.99. The second data set (remaining 21 points) changes to a 3 parameter Weibull with an R^2 value somewhere in the neighborhood of 0.976. So my questions are
1) What is the minimum sample size you need to accurately represent the population? For example from this sample size X the PDF is within some metric (std deviations, % etc) of the true PDF. Clearly R^2 value alone isn’t a good metric
2) I would like to plot the remaining 21 data points over the CDF calculated from my first 5 points. I have used 2 methods. Simply calculating the MR and plotting test cycle vs MR. The second using the Beta and Eta to calculate the CDF percent and plotting test cycle vs CDF percentile. Is there a good way to represent predicted CDF vs test data?
Here is my data set.
154173
171158
83431
201778
117578
192083
136262
149487
148009
98317
69798
94195
62548
103574
108364
132377
143047
85272
95760
214166
289237
161265
172490
99972
117440
89717





RE: What is the minimum sample size to generate a Weibull distribution?
2) Typically, you plot the data over the predicted equation curve
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RE: What is the minimum sample size to generate a Weibull distribution?
RE: What is the minimum sample size to generate a Weibull distribution?
This practice could be seen as putting the cart before the horse. Be careful not to force inadequate data into reinforcing unsubstantiated foregone conclusions that your model can be in fact described by a Wiebull distribution.
RE: What is the minimum sample size to generate a Weibull distribution?
Using MSE are you suggested I get 0.009 and I don't think the 5 data points accurately predicts the remaining 21.
How do you plot the remaining 21 points over the predictive CDF? What method do you use to calculate the Median ranking?
RE: What is the minimum sample size to generate a Weibull distribution?
RE: What is the minimum sample size to generate a Weibull distribution?
Offhand, I would argue that 5 data points would be woefully inadequate for fitting 3 parameters; a minimum of 3 times the number of parameters would seem like a good place to start, but even then, their spacing and relative similarity need to be considered. Since "noise" is inherent in any sort of reliability data, more data points
If you look at your data more closely, you can see that there is one specific datapoint that is problematic, because it seems to be substantially different than the rest.
TTFN

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RE: What is the minimum sample size to generate a Weibull distribution?
The first 5 data points I used a 2 parameter and for the remaining 21 I used 3 parameter based on my regression values. A lot of these seems to be based on your median rankings.
RE: What is the minimum sample size to generate a Weibull distribution?
TTFN

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RE: What is the minimum sample size to generate a Weibull distribution?
If you know your data fits some Weibull curve, plot it. Then see what data values don't land on it.
If you don't know which Weibull curve is the correct one, changing sample size will just keep on giving you different Weibull curves, each with slightly different parameters than the other.
To arrive at a Weibull curve that best describes a set of n values, consider all n values and calculate Weibull parameters.
If introducing new values to the sample size doesn't introduce disproportionate noise to the point where the curve doesn't change much from the previous curve, ie. the curve's parameters do ot change significantly, then you've got enough samples to predict the curve described by all (and presumably future) samples.
RE: What is the minimum sample size to generate a Weibull distribution?
RE: What is the minimum sample size to generate a Weibull distribution?
If you have a sample of data and you calculate the best fit curve, it will be the best fit curve for the sample of data you have. If you change the data set and do it again, it will be the best fit curve for that data set.
If you are convinced that the Weibull curve that fits the whole sample population is the "ONE" true curve, take 5 random values from your population, get the parameters for the best Weibull fit. Now take six different, random values and calculate the Weibull parameters for that set. Keep on doing that with ever more and more random values. When you see that Weibull's parameters aren't changing much (within your margin of error), you've discovered how many values you need.
RE: What is the minimum sample size to generate a Weibull distribution?
TTFN

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RE: What is the minimum sample size to generate a Weibull distribution?
TTFN

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RE: What is the minimum sample size to generate a Weibull distribution?