21 Sep '17 09:415 edits

In my research, I have derived the equations for HUNDREDS of totally new probability distributions (new to statistics) all of which I intend to publish in my book.

I have discovered some have unusual properties.

But now I have discovered one that by far has the weirdest property of them all!

I have discovered so many new distributions that I had to invent a systematic set of naming protocols (which I will explain in my book) else naming all of them would be totally arbitrary and chaotic. Using that systematic set of naming protocols, I call this particular probability distribution "One_up_i_u_outy_xteed".

But when I tried to derive the equation for its median using the usual old tried and tested and trusted methods for finding the median of any distribution, I found that for certain (but not all) input values, the resulting median equation I derived seems to be complete gibberish! It seemed to be saying that the median can be not only as much as "+infinity" but actually OVER "+infinity" !!!

And yet random variable x for this distribution must be finite i.e. x cannot be infinity.

Initially I naturally thought I must be doing something wrong with the maths so I have spend the last week with increasing frustration trying to see what I was doing wrong with my maths. But now I discovered it isn't the maths that is wrong but the assumption that it HAS a median! Although the distribution DOES normalize for all allowed input values, (I have checked this thoroughly) its cumulative distribution function has some extremely subtly weird properties for some of those input values that is such as to render all quantiles meaningless and "undefined" including for its median!

But now, here is my question;

Is my discovery truly unique or are there any known numerical probability distribution already discovered that sometimes have no definable median? Example?

I have discovered some have unusual properties.

But now I have discovered one that by far has the weirdest property of them all!

I have discovered so many new distributions that I had to invent a systematic set of naming protocols (which I will explain in my book) else naming all of them would be totally arbitrary and chaotic. Using that systematic set of naming protocols, I call this particular probability distribution "One_up_i_u_outy_xteed".

But when I tried to derive the equation for its median using the usual old tried and tested and trusted methods for finding the median of any distribution, I found that for certain (but not all) input values, the resulting median equation I derived seems to be complete gibberish! It seemed to be saying that the median can be not only as much as "+infinity" but actually OVER "+infinity" !!!

And yet random variable x for this distribution must be finite i.e. x cannot be infinity.

Initially I naturally thought I must be doing something wrong with the maths so I have spend the last week with increasing frustration trying to see what I was doing wrong with my maths. But now I discovered it isn't the maths that is wrong but the assumption that it HAS a median! Although the distribution DOES normalize for all allowed input values, (I have checked this thoroughly) its cumulative distribution function has some extremely subtly weird properties for some of those input values that is such as to render all quantiles meaningless and "undefined" including for its median!

But now, here is my question;

Is my discovery truly unique or are there any known numerical probability distribution already discovered that sometimes have no definable median? Example?