Records in the presence of a linear trend

1987 ◽  
Vol 19 (4) ◽  
pp. 801-828 ◽  
Author(s):  
Rocco Ballerini ◽  
Sidney I. Resnick
Keyword(s):  
Gaussian Process ◽  
Limit Theorems ◽  
Linear Trend ◽  
Random Sequence ◽  
Record Values ◽  
Stationary Gaussian Process ◽  
Record Times

Records from the sequence Yn = Xn + cn, n ≧ 1 are analyzed, where {Xn} is a strictly stationary random sequence. We prove various limit theorems for the record rate, record times, and record values. The situation when {Xn} is a stationary Gaussian process is considered with special attention given to Gaussian ARMA sequences. Data for the 400 and 800 metre races are used to illustrate these results.

Records in the presence of a linear trend

1987 ◽  
Vol 19 (04) ◽  
pp. 801-828 ◽  
Author(s):  
Rocco Ballerini ◽  
Sidney I. Resnick
Keyword(s):  
Gaussian Process ◽  
Limit Theorems ◽  
Linear Trend ◽  
Random Sequence ◽  
Record Values ◽  
Stationary Gaussian Process ◽  
Record Times

Records from the sequence Yn = Xn + cn, n ≧ 1 are analyzed, where {Xn } is a strictly stationary random sequence. We prove various limit theorems for the record rate, record times, and record values. The situation when {Xn } is a stationary Gaussian process is considered with special attention given to Gaussian ARMA sequences. Data for the 400 and 800 metre races are used to illustrate these results.

Embedding sequences of successive maxima in extremal processes, with applications

1987 ◽  
Vol 24 (4) ◽  
pp. 827-837 ◽  
Author(s):  
Rocco Ballerini ◽  
Sidney I. Resnick
Keyword(s):  
Population Size ◽  
Limit Theorems ◽  
Random Variables ◽  
Record Values ◽  
Record Times ◽  
Extremal Processes ◽  
Sample Record

Consequences of embedding sequences {Mn} in an extremal-F process are discussed where Mn represents the maximum of n independent (but not necessarily identically distributed) random variables. Various limit theorems are proved for the sample record rate, record times, inter-record times, and record values. These results are illustrated with applications to three particular record models: the Yang (1975) record model where population size increases geometrically, a record model where linear improvement is present, and a record model incorporating features of the previous two.

Embedding sequences of successive maxima in extremal processes, with applications

1987 ◽  
Vol 24 (04) ◽  
pp. 827-837 ◽  
Author(s):  
Rocco Ballerini ◽  
Sidney I. Resnick
Keyword(s):  
Population Size ◽  
Limit Theorems ◽  
Random Variables ◽  
Record Values ◽  
Record Times ◽  
Extremal Processes ◽  
Sample Record

Consequences of embedding sequences {Mn } in an extremal-F process are discussed where Mn represents the maximum of n independent (but not necessarily identically distributed) random variables. Various limit theorems are proved for the sample record rate, record times, inter-record times, and record values. These results are illustrated with applications to three particular record models: the Yang (1975) record model where population size increases geometrically, a record model where linear improvement is present, and a record model incorporating features of the previous two.

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