Sequential Estimation of a Continuous Distribution Function from Delayed Observations

2011 ◽  
Vol 40 (10) ◽  
pp. 1717-1733 ◽  
Author(s):  
Agnieszka Stępień-Baran
Keyword(s):  
Distribution Function ◽  
Continuous Distribution ◽  
Sequential Estimation ◽  
Continuous Distribution Function

New method for the restoration of the continuous distribution function of hyperfine fields andits possibilities

1993 ◽  
Vol 78 (1-4) ◽  
pp. 391-396 ◽  
Author(s):  
S. D. Antipov ◽  
G. E. Gorjunov ◽  
A. F. Djura ◽  
Ju. M. Polukarov ◽  
D. V. Sadkov ◽  
...  
Keyword(s):  
Distribution Function ◽  
Continuous Distribution ◽  
New Method ◽  
Continuous Distribution Function ◽  
Hyperfine Fields

Records from a power model of independent observations

1995 ◽  
Vol 32 (4) ◽  
pp. 982-990 ◽  
Author(s):  
Ishay Weissman
Keyword(s):  
Distribution Function ◽  
Wide Spectrum ◽  
Continuous Distribution ◽  
Random Variables ◽  
Continuous Distribution Function ◽  
Power Model ◽  
Record Times ◽  
Independent Sequence ◽  
Independent Observations

Records from are analyzed, where {Yj} is an independent sequence of random variables. Each Yj has a continuous distribution function Fj = Fλj for some distribution F and some λ j > 0. We study records, record times and related quantities for this sequence. Depending on the sequence of powers , a wide spectrum of behaviour is exhibited.

On the law of the iterated logarithm for inter-record times

1970 ◽  
Vol 7 (02) ◽  
pp. 432-439 ◽  
Author(s):  
William E. Strawderman ◽  
Paul T. Holmes
Keyword(s):  
Distribution Function ◽  
Probability Space ◽  
Continuous Distribution ◽  
Random Variables ◽  
Continuous Distribution Function ◽  
Record Times ◽  
Iterated Logarithm ◽  
The Law ◽  
Image Position ◽  
Independent Identically Distributed

Let X 1, X2, X 3 , ··· be independent, identically distributed random variables on a probability space (Ω, F, P); and with a continuous distribution function. Let the sequence of indices {Vr } be defined as Also define The following theorem is due to Renyi [5].

scholarly journals On the number and sum of near-record observations

2005 ◽  
Vol 37 (03) ◽  
pp. 765-780 ◽  
Author(s):  
N. Balakrishnan ◽  
A.G. Pakes ◽  
A. Stepanov
Keyword(s):  
Distribution Function ◽  
Asymptotic Properties ◽  
Continuous Distribution ◽  
Random Variables ◽  
Continuous Distribution Function ◽  
Record Time ◽  
Record Value ◽  
Independent And Identically Distributed

Let X 1,X 2,… be a sequence of independent and identically distributed random variables with some continuous distribution function F. Let L(n) and X(n) denote the nth record time and the nth record value, respectively. We refer to the variables X i as near-nth-record observations if X i ∈(X(n)-a,X(n)], with a>0, and L(n)<i<L(n+1). In this work we study asymptotic properties of the number of near-record observations. We also discuss sums of near-record observations.

On record values and the exponent of a distribution with regularly varying upper tail

1992 ◽  
Vol 29 (3) ◽  
pp. 575-586 ◽  
Author(s):  
Mohamed Berred
Keyword(s):  
Distribution Function ◽  
Asymptotic Behaviour ◽  
Continuous Distribution ◽  
Random Variables ◽  
Record Values ◽  
Numerical Results ◽  
Continuous Distribution Function ◽  
Regularly Varying

Let {Xn, n ≧ 1} be an i.i.d. sequence of positive random variables with a continuous distribution function having a regularly varying upper tail. Denote by {X(n), n ≧ 1} the corresponding sequence of record values. We introduce two statistics based on the sequence of successive record values and investigate their asymptotic behaviour. We also give some numerical results.

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