27 Jan '16 11:2012 edits

can anyone give me an example of a continuous probability distribution that has no definable mode or modes?

I am note talking here about, say, a continuous uniform distribution, which arguably has an infinite number of modes along a 'plateau' on its probability density function thus merely has no

I believe I may have found (or more like ~invented) such a type of 'modeless' continuous distribution (which I have named an "expon paracav" ) because where the random variable X value has its highest point on the graph for its probability density equation, its 'apparent' mode value (X=0 in this case) if mathematically applied/interpreted naively, is not allowed else this leads to an epistemological contradiction. But I wondered how unusual or unique that property is. So I search the net for another example of a 'modeless' continuous distribution but got absolutely nowhere.

Anyone?

I am note talking here about, say, a continuous uniform distribution, which arguably has an infinite number of modes along a 'plateau' on its probability density function thus merely has no

*unique*mode/modes. I am talking here about a continuous distribution that*literally*has*no valid/definable*mode/modes whatsoever!I believe I may have found (or more like ~invented) such a type of 'modeless' continuous distribution (which I have named an "expon paracav" ) because where the random variable X value has its highest point on the graph for its probability density equation, its 'apparent' mode value (X=0 in this case) if mathematically applied/interpreted naively, is not allowed else this leads to an epistemological contradiction. But I wondered how unusual or unique that property is. So I search the net for another example of a 'modeless' continuous distribution but got absolutely nowhere.

Anyone?