scholarly journals Why indeterminate probability is rational

2009 ◽  
Vol 7 (4) ◽  
pp. 364-376 ◽  
Author(s):  
Isaac Levi
Keyword(s):  
Indeterminate Probability

Stieltjes classes for moment-indeterminate probability distributions

2004 ◽  
Vol 41 (A) ◽  
pp. 281-294 ◽  
Author(s):  
Jordan Stoyanov
Keyword(s):  
Probability Distributions ◽  
Classical Problem ◽  
Inverse Gaussian ◽  
Positive Order ◽  
Power Transformations ◽  
Log Normal ◽  
Open Question ◽  
Indeterminate Probability ◽  
Index Of Dissimilarity ◽  
Finite Moments

Let F be a probability distribution function with density f. We assume that (a) F has finite moments of any integer positive order and (b) the classical problem of moments for F has a nonunique solution (F is M-indeterminate). Our goal is to describe a , where h is a ‘small' perturbation function. Such a class S consists of different distributions Fε (fε is the density of Fε) all sharing the same moments as those of F, thus illustrating the nonuniqueness of F, and of any Fε, in terms of the moments. Power transformations of distributions such as the normal, log-normal and exponential are considered and for them Stieltjes classes written explicitly. We define a characteristic of S called an index of dissimilarity and calculate its value in some cases. A new Stieltjes class involving a power of the normal distribution is presented. An open question about the inverse Gaussian distribution is formulated. Related topics are briefly discussed.

Fallacy and controversy about base rates

1996 ◽  
Vol 19 (1) ◽  
pp. 31-32 ◽  
Author(s):  
Isaac Levi
Keyword(s):  
Base Rate ◽  
Probability Judgment ◽  
Reference Class ◽  
Probability Judgments ◽  
Base Rates ◽  
Target Article ◽  
Class Information ◽  
The Difference ◽  
Indeterminate Probability

AbstractKoehler's target article attempts a balanced view of the relevance of knowledge of base rates to judgments of subjective or credal probability, but he is not sensitive enough to the difference between requiring and permitting the equation of probability judgments with base rates, the interaction between precision of base rate and reference class information, and the possibility of indeterminate probability judgment.

Stieltjes classes for moment-indeterminate probability distributions

2004 ◽  
Vol 41 (A) ◽  
pp. 281-294 ◽  
Author(s):  
Jordan Stoyanov
Keyword(s):  
Probability Distributions ◽  
Classical Problem ◽  
Inverse Gaussian ◽  
Positive Order ◽  
Power Transformations ◽  
Log Normal ◽  
Open Question ◽  
Indeterminate Probability ◽  
Index Of Dissimilarity ◽  
Finite Moments

Let F be a probability distribution function with density f. We assume that (a) F has finite moments of any integer positive order and (b) the classical problem of moments for F has a nonunique solution (F is M-indeterminate). Our goal is to describe a , where h is a ‘small' perturbation function. Such a class S consists of different distributions Fε (fε is the density of Fε ) all sharing the same moments as those of F, thus illustrating the nonuniqueness of F, and of any Fε, in terms of the moments. Power transformations of distributions such as the normal, log-normal and exponential are considered and for them Stieltjes classes written explicitly. We define a characteristic of S called an index of dissimilarity and calculate its value in some cases. A new Stieltjes class involving a power of the normal distribution is presented. An open question about the inverse Gaussian distribution is formulated. Related topics are briefly discussed.

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