Vito Ricci
2004-Dec-02 10:07 UTC
[R] Re: A somewhat off the line question to a log normal distribution
Dear Siegfried, I believe your boss is wrong saying that:>He also tried to explain me that the monthly means >(based on the daily measurements) must follow a >log-normal distribution too then over the course of ayear. every statistician know that increasing the sample size the sample distribution of the mean is proxy to a gaussian distribution (Central Limit Theorem) independently from the original distribution of data (in your case log-normal). See this: The Central Limit Theorem is a statement about the characteristics of the sampling distribution of means of random samples from a given population. That is, it describes the characteristics of the distribution of values we would obtain if we were able to draw an infinite number of random samples of a given size from a given population and we calculated the mean of each sample. The Central Limit Theorem consists of three statements: [1] The mean of the sampling distribution of means is equal to the mean of the population from which the samples were drawn. [2] The variance of the sampling distribution of means is equal to the variance of the population from which the samples were drawn divided by the size of the samples. --> [3] If the original population is distributed normally (i.e. it is bell shaped), the sampling distribution of means will also be normal. If the original population is not normally distributed, the sampling distribution of means will increasingly approximate a normal distribution as sample size increases. (i.e. when increasingly large samples are drawn) <-- So results you got are just in this way! I think your boss doesn't know well statistics! Regards Vito You wrote: Hello: Oh yes I know it isn't so much related to R, but I gather there are a lot of statisticians reading the mailing list. My boss repeatedly tried to explain me the following. =Lets assume you have got daily measurements of a variable in natural sciences. It turned out that the aformentioned daily measurements follow a log-normal distribution when considered over the course of a year. Okay. He also tried to explain me that the monthly means (based on the daily measurements) must follow a log-normal distribution too then over the course of a year. = I somehow get his explanation. But I have measurements which are log-normal distributed when evaluated on a daily basis over the course of a year but they are close to a Gaussian distribution when considered under the light of monthly means over the course of a year. Is such a latter case feasible. And if not why. Regards, Siegfried Gonzi ====Diventare costruttori di soluzioni Became solutions' constructors "The business of the statistician is to catalyze the scientific learning process." George E. P. Box Visitate il portale http://www.modugno.it/ e in particolare la sezione su Palese http://www.modugno.it/archivio/palese/
Phineas Campbell
2004-Dec-02 12:42 UTC
[R] Re: A somewhat off the line question to a log normal distribution
It has always been my understanding that an arbitrary lognormal distribution has a sufficient quantity of finite moments to ensure a CLT holds, it is not uniquely defined by these moments. Thus although sums of IID lognormal variates will converge to a normal distribution we cannot know, a priori, what the parameters of this distribution will be. If a distribution is strictly positive and has sufficient moments then the sums of logs of the variables will converge to a normal distribution, thus in estimating parameters that are closely related to the mean there would appear to be little to loose by logging the data. Phineas Campbell -----Original Message----- From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at stat.math.ethz.ch]On Behalf Of Vito Ricci Sent: Thursday, December 02, 2004 10:08 AM To: r-help at stat.math.ethz.ch Subject: [R] Re: A somewhat off the line question to a log normal distribution Dear Siegfried, I believe your boss is wrong saying that:>He also tried to explain me that the monthly means >(based on the daily measurements) must follow a >log-normal distribution too then over the course of ayear. every statistician know that increasing the sample size the sample distribution of the mean is proxy to a gaussian distribution (Central Limit Theorem) independently from the original distribution of data (in your case log-normal). See this: The Central Limit Theorem is a statement about the characteristics of the sampling distribution of means of random samples from a given population. That is, it describes the characteristics of the distribution of values we would obtain if we were able to draw an infinite number of random samples of a given size from a given population and we calculated the mean of each sample. The Central Limit Theorem consists of three statements: [1] The mean of the sampling distribution of means is equal to the mean of the population from which the samples were drawn. [2] The variance of the sampling distribution of means is equal to the variance of the population from which the samples were drawn divided by the size of the samples. --> [3] If the original population is distributed normally (i.e. it is bell shaped), the sampling distribution of means will also be normal. If the original population is not normally distributed, the sampling distribution of means will increasingly approximate a normal distribution as sample size increases. (i.e. when increasingly large samples are drawn) <-- So results you got are just in this way! I think your boss doesn't know well statistics! Regards Vito You wrote: Hello: Oh yes I know it isn't so much related to R, but I gather there are a lot of statisticians reading the mailing list. My boss repeatedly tried to explain me the following. =Lets assume you have got daily measurements of a variable in natural sciences. It turned out that the aformentioned daily measurements follow a log-normal distribution when considered over the course of a year. Okay. He also tried to explain me that the monthly means (based on the daily measurements) must follow a log-normal distribution too then over the course of a year. = I somehow get his explanation. But I have measurements which are log-normal distributed when evaluated on a daily basis over the course of a year but they are close to a Gaussian distribution when considered under the light of monthly means over the course of a year. Is such a latter case feasible. And if not why. Regards, Siegfried Gonzi ====Diventare costruttori di soluzioni Became solutions' constructors "The business of the statistician is to catalyze the scientific learning process." George E. P. Box Visitate il portale http://www.modugno.it/ e in particolare la sezione su Palese http://www.modugno.it/archivio/palese/ ______________________________________________ R-help at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html