Mixing
How to calculate peakiness or uniformity in histogram?
$begingroup$
I have a histogram with 20 bins ranging from -1 to 1 with an interval of 0.1.
I would like to know if the histogram distribution is uniform or is peaked.
I want to compare several such histograms and take the one which has more "uniform" distribution and less peaks.
Any suggestions on how to proceed ?
statistics statistical-inference
asked Sep 6 '14 at 3:55
SaiSai
84
$endgroup$
add a comment |
$begingroup$
I have a histogram with 20 bins ranging from -1 to 1 with an interval of 0.1.
I would like to know if the histogram distribution is uniform or is peaked.
I want to compare several such histograms and take the one which has more "uniform" distribution and less peaks.
Any suggestions on how to proceed ?
statistics statistical-inference
asked Sep 6 '14 at 3:55
SaiSai
84
$endgroup$
$begingroup$
Test the goodness of fit of the histogram to a uniform distribution?
$endgroup$
– Rahul
Sep 6 '14 at 4:04
$begingroup$
Thank you, i think it almost fits my need. But I heard of this word "peakiness test" but cannot get any reliable and exact information to use it . Do you know about it ?
$endgroup$
– Sai
Sep 6 '14 at 4:26
$begingroup$
You may also want to see this answer to the question "How does one measure the non-uniformity of a distribution?".
$endgroup$
– r.e.s.
Sep 6 '14 at 4:37
$begingroup$
Thank you, its a nice pointer, i ll explore this option.
$endgroup$
– Sai
Sep 6 '14 at 4:44
add a comment |
$begingroup$
I have a histogram with 20 bins ranging from -1 to 1 with an interval of 0.1.
I would like to know if the histogram distribution is uniform or is peaked.
I want to compare several such histograms and take the one which has more "uniform" distribution and less peaks.
Any suggestions on how to proceed ?
statistics statistical-inference
asked Sep 6 '14 at 3:55
SaiSai
84
$endgroup$
I have a histogram with 20 bins ranging from -1 to 1 with an interval of 0.1.
I would like to know if the histogram distribution is uniform or is peaked.
I want to compare several such histograms and take the one which has more "uniform" distribution and less peaks.
Any suggestions on how to proceed ?
statistics statistical-inference
statistics statistical-inference
asked Sep 6 '14 at 3:55
SaiSai
84
asked Sep 6 '14 at 3:55
SaiSai
84
asked Sep 6 '14 at 3:55
SaiSai
84
asked Sep 6 '14 at 3:55
SaiSai
84
asked Sep 6 '14 at 3:55
SaiSai
84
84
$begingroup$
Test the goodness of fit of the histogram to a uniform distribution?
$endgroup$
– Rahul
Sep 6 '14 at 4:04
$begingroup$
Thank you, i think it almost fits my need. But I heard of this word "peakiness test" but cannot get any reliable and exact information to use it . Do you know about it ?
$endgroup$
– Sai
Sep 6 '14 at 4:26
$begingroup$
You may also want to see this answer to the question "How does one measure the non-uniformity of a distribution?".
$endgroup$
– r.e.s.
Sep 6 '14 at 4:37
$begingroup$
Thank you, its a nice pointer, i ll explore this option.
$endgroup$
– Sai
Sep 6 '14 at 4:44
add a comment |
$begingroup$
Test the goodness of fit of the histogram to a uniform distribution?
$endgroup$
– Rahul
Sep 6 '14 at 4:04
$begingroup$
Thank you, i think it almost fits my need. But I heard of this word "peakiness test" but cannot get any reliable and exact information to use it . Do you know about it ?
$endgroup$
– Sai
Sep 6 '14 at 4:26
$begingroup$
You may also want to see this answer to the question "How does one measure the non-uniformity of a distribution?".
$endgroup$
– r.e.s.
Sep 6 '14 at 4:37
$begingroup$
Thank you, its a nice pointer, i ll explore this option.
$endgroup$
– Sai
Sep 6 '14 at 4:44
$begingroup$
Test the goodness of fit of the histogram to a uniform distribution?
$endgroup$
– Rahul
Sep 6 '14 at 4:04
$begingroup$
Test the goodness of fit of the histogram to a uniform distribution?
$endgroup$
– Rahul
Sep 6 '14 at 4:04
$begingroup$
Thank you, i think it almost fits my need. But I heard of this word "peakiness test" but cannot get any reliable and exact information to use it . Do you know about it ?
$endgroup$
– Sai
Sep 6 '14 at 4:26
$begingroup$
Thank you, i think it almost fits my need. But I heard of this word "peakiness test" but cannot get any reliable and exact information to use it . Do you know about it ?
$endgroup$
– Sai
Sep 6 '14 at 4:26
$begingroup$
You may also want to see this answer to the question "How does one measure the non-uniformity of a distribution?".
$endgroup$
– r.e.s.
Sep 6 '14 at 4:37
$begingroup$
You may also want to see this answer to the question "How does one measure the non-uniformity of a distribution?".
$endgroup$
– r.e.s.
Sep 6 '14 at 4:37
$begingroup$
Thank you, its a nice pointer, i ll explore this option.
$endgroup$
– Sai
Sep 6 '14 at 4:44
$begingroup$
Thank you, its a nice pointer, i ll explore this option.
$endgroup$
– Sai
Sep 6 '14 at 4:44
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The answer depends on what you are trying to do:
- Are you trying to infer which histogram was mostly likely to be generated by a uniform distribution OR
- Trying to find which histogram demonstrates the least non-uniformity?
These questions may seem the same, but they are not. Inference is very sensitive to the sample size, whereas descriptive measure take the data at face value.
If you are going for (1), then the suggestions in the comments or link will work fine. However, if you are trying to find the most uniform histogram, then this is not an inference problem, but a measurement problem...how do you measure non-uniformity?
At the risk of appearing shamelessly self-promoting, I recently answered a similar question by describing a method I developed to rand distributions by their degree of uniformity. Take a look and see if you think it is relevant to your problem.
edited Apr 13 '17 at 12:21
Community♦
1
$endgroup$
$begingroup$
I am trying to tackle the second one as mentioned in your answer. Could you tell why skewness or kurtosis cannot be a good measure ?
$endgroup$
– Sai
Sep 8 '14 at 3:00
$begingroup$
@Sai the problem with moment-based measures is that they are not unique. The most uniform distribution will certainly lack skew, but kurtosis is not easy to relate directly with uniformity...two distributions can have similar kurtosis but look very different. The path length method I use is based on a key feature of uniformity: its cdf is maximally linear given the constraints.
$endgroup$
– user76844
Sep 8 '14 at 3:48
add a comment |
$begingroup$
One possible approach would be to use the Chi-square test to compare the "observed" histogram counts with the "expected" uniform distribution.
The chi-square test statistic or its p-value may be used as a possible metric of "(non)uniformness" - highly non-uniform histograms would tend to have high chi-square values and the corresponding p-values approaching zero.
In Python:
from scipy.stats import chisquare
uniformness = chisquare(counts_vector).pvalue
answered Jan 25 at 0:02
KT.KT.
13616
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The answer depends on what you are trying to do:
- Are you trying to infer which histogram was mostly likely to be generated by a uniform distribution OR
- Trying to find which histogram demonstrates the least non-uniformity?
These questions may seem the same, but they are not. Inference is very sensitive to the sample size, whereas descriptive measure take the data at face value.
If you are going for (1), then the suggestions in the comments or link will work fine. However, if you are trying to find the most uniform histogram, then this is not an inference problem, but a measurement problem...how do you measure non-uniformity?
At the risk of appearing shamelessly self-promoting, I recently answered a similar question by describing a method I developed to rand distributions by their degree of uniformity. Take a look and see if you think it is relevant to your problem.
edited Apr 13 '17 at 12:21
Community♦
1
$endgroup$
$begingroup$
I am trying to tackle the second one as mentioned in your answer. Could you tell why skewness or kurtosis cannot be a good measure ?
$endgroup$
– Sai
Sep 8 '14 at 3:00
$begingroup$
@Sai the problem with moment-based measures is that they are not unique. The most uniform distribution will certainly lack skew, but kurtosis is not easy to relate directly with uniformity...two distributions can have similar kurtosis but look very different. The path length method I use is based on a key feature of uniformity: its cdf is maximally linear given the constraints.
$endgroup$
– user76844
Sep 8 '14 at 3:48
add a comment |
$begingroup$
The answer depends on what you are trying to do:
- Are you trying to infer which histogram was mostly likely to be generated by a uniform distribution OR
- Trying to find which histogram demonstrates the least non-uniformity?
These questions may seem the same, but they are not. Inference is very sensitive to the sample size, whereas descriptive measure take the data at face value.
If you are going for (1), then the suggestions in the comments or link will work fine. However, if you are trying to find the most uniform histogram, then this is not an inference problem, but a measurement problem...how do you measure non-uniformity?
At the risk of appearing shamelessly self-promoting, I recently answered a similar question by describing a method I developed to rand distributions by their degree of uniformity. Take a look and see if you think it is relevant to your problem.
edited Apr 13 '17 at 12:21
Community♦
1
$endgroup$
$begingroup$
I am trying to tackle the second one as mentioned in your answer. Could you tell why skewness or kurtosis cannot be a good measure ?
$endgroup$
– Sai
Sep 8 '14 at 3:00
$begingroup$
@Sai the problem with moment-based measures is that they are not unique. The most uniform distribution will certainly lack skew, but kurtosis is not easy to relate directly with uniformity...two distributions can have similar kurtosis but look very different. The path length method I use is based on a key feature of uniformity: its cdf is maximally linear given the constraints.
$endgroup$
– user76844
Sep 8 '14 at 3:48
add a comment |
$begingroup$
The answer depends on what you are trying to do:
- Are you trying to infer which histogram was mostly likely to be generated by a uniform distribution OR
- Trying to find which histogram demonstrates the least non-uniformity?
These questions may seem the same, but they are not. Inference is very sensitive to the sample size, whereas descriptive measure take the data at face value.
If you are going for (1), then the suggestions in the comments or link will work fine. However, if you are trying to find the most uniform histogram, then this is not an inference problem, but a measurement problem...how do you measure non-uniformity?
At the risk of appearing shamelessly self-promoting, I recently answered a similar question by describing a method I developed to rand distributions by their degree of uniformity. Take a look and see if you think it is relevant to your problem.
edited Apr 13 '17 at 12:21
Community♦
1
$endgroup$
The answer depends on what you are trying to do:
- Are you trying to infer which histogram was mostly likely to be generated by a uniform distribution OR
- Trying to find which histogram demonstrates the least non-uniformity?
These questions may seem the same, but they are not. Inference is very sensitive to the sample size, whereas descriptive measure take the data at face value.
If you are going for (1), then the suggestions in the comments or link will work fine. However, if you are trying to find the most uniform histogram, then this is not an inference problem, but a measurement problem...how do you measure non-uniformity?
At the risk of appearing shamelessly self-promoting, I recently answered a similar question by describing a method I developed to rand distributions by their degree of uniformity. Take a look and see if you think it is relevant to your problem.
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
1
answered Sep 6 '14 at 5:25
user76844
$begingroup$
I am trying to tackle the second one as mentioned in your answer. Could you tell why skewness or kurtosis cannot be a good measure ?
$endgroup$
– Sai
Sep 8 '14 at 3:00
$begingroup$
@Sai the problem with moment-based measures is that they are not unique. The most uniform distribution will certainly lack skew, but kurtosis is not easy to relate directly with uniformity...two distributions can have similar kurtosis but look very different. The path length method I use is based on a key feature of uniformity: its cdf is maximally linear given the constraints.
$endgroup$
– user76844
Sep 8 '14 at 3:48
add a comment |
$begingroup$
I am trying to tackle the second one as mentioned in your answer. Could you tell why skewness or kurtosis cannot be a good measure ?
$endgroup$
– Sai
Sep 8 '14 at 3:00
$begingroup$
@Sai the problem with moment-based measures is that they are not unique. The most uniform distribution will certainly lack skew, but kurtosis is not easy to relate directly with uniformity...two distributions can have similar kurtosis but look very different. The path length method I use is based on a key feature of uniformity: its cdf is maximally linear given the constraints.
$endgroup$
– user76844
Sep 8 '14 at 3:48
$begingroup$
I am trying to tackle the second one as mentioned in your answer. Could you tell why skewness or kurtosis cannot be a good measure ?
$endgroup$
– Sai
Sep 8 '14 at 3:00
$begingroup$
I am trying to tackle the second one as mentioned in your answer. Could you tell why skewness or kurtosis cannot be a good measure ?
$endgroup$
– Sai
Sep 8 '14 at 3:00
$begingroup$
@Sai the problem with moment-based measures is that they are not unique. The most uniform distribution will certainly lack skew, but kurtosis is not easy to relate directly with uniformity...two distributions can have similar kurtosis but look very different. The path length method I use is based on a key feature of uniformity: its cdf is maximally linear given the constraints.
$endgroup$
– user76844
Sep 8 '14 at 3:48
$begingroup$
@Sai the problem with moment-based measures is that they are not unique. The most uniform distribution will certainly lack skew, but kurtosis is not easy to relate directly with uniformity...two distributions can have similar kurtosis but look very different. The path length method I use is based on a key feature of uniformity: its cdf is maximally linear given the constraints.
$endgroup$
– user76844
Sep 8 '14 at 3:48
add a comment |
$begingroup$
One possible approach would be to use the Chi-square test to compare the "observed" histogram counts with the "expected" uniform distribution.
The chi-square test statistic or its p-value may be used as a possible metric of "(non)uniformness" - highly non-uniform histograms would tend to have high chi-square values and the corresponding p-values approaching zero.
In Python:
from scipy.stats import chisquare
uniformness = chisquare(counts_vector).pvalue
answered Jan 25 at 0:02
KT.KT.
13616
$endgroup$
add a comment |
$begingroup$
One possible approach would be to use the Chi-square test to compare the "observed" histogram counts with the "expected" uniform distribution.
The chi-square test statistic or its p-value may be used as a possible metric of "(non)uniformness" - highly non-uniform histograms would tend to have high chi-square values and the corresponding p-values approaching zero.
In Python:
from scipy.stats import chisquare
uniformness = chisquare(counts_vector).pvalue
answered Jan 25 at 0:02
KT.KT.
13616
$endgroup$
add a comment |
$begingroup$
One possible approach would be to use the Chi-square test to compare the "observed" histogram counts with the "expected" uniform distribution.
The chi-square test statistic or its p-value may be used as a possible metric of "(non)uniformness" - highly non-uniform histograms would tend to have high chi-square values and the corresponding p-values approaching zero.
In Python:
from scipy.stats import chisquare
uniformness = chisquare(counts_vector).pvalue
answered Jan 25 at 0:02
KT.KT.
13616
$endgroup$
One possible approach would be to use the Chi-square test to compare the "observed" histogram counts with the "expected" uniform distribution.
The chi-square test statistic or its p-value may be used as a possible metric of "(non)uniformness" - highly non-uniform histograms would tend to have high chi-square values and the corresponding p-values approaching zero.
In Python:
from scipy.stats import chisquare
uniformness = chisquare(counts_vector).pvalue
answered Jan 25 at 0:02
KT.KT.
13616
answered Jan 25 at 0:02
KT.KT.
13616
answered Jan 25 at 0:02
KT.KT.
13616
answered Jan 25 at 0:02
KT.KT.
13616
13616
add a comment |
add a comment |
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$begingroup$
Test the goodness of fit of the histogram to a uniform distribution?
$endgroup$
– Rahul
Sep 6 '14 at 4:04
$begingroup$
Thank you, i think it almost fits my need. But I heard of this word "peakiness test" but cannot get any reliable and exact information to use it . Do you know about it ?
$endgroup$
– Sai
Sep 6 '14 at 4:26
$begingroup$
You may also want to see this answer to the question "How does one measure the non-uniformity of a distribution?".
$endgroup$
– r.e.s.
Sep 6 '14 at 4:37
$begingroup$
Thank you, its a nice pointer, i ll explore this option.
$endgroup$
– Sai
Sep 6 '14 at 4:44