berkson: alpha-particle emissions of Americurium-241
In Auburngrads/SMRD: Statistical Methods For Reliability Data
Description
Berkson investigated the randomness of alpha-particle
emissions of Americium-241 (which has a half-life of about 458 years).
Physical theory suggests that, over a short period of time, the
interarrival times of observed particles would be independent and come
from an exponential distribution where the rate parameter is the mean
time between arrivals. The corresponding homogeneous Poisson process that
counts the number of emissions on the real-time line has arrival rate or
the intensity lambda=1/theta. The data consist of 10,220 observed interarrival
times of alpha particles (time unit equal to 1/5,000 second). The observed
interarrival times were put into intervals (or bins) running from 0 to 4,000
time units with interval lengths ranging from 25 to 100 time units, with one
additional interval for observed times exceeding 4,000 time units. To save space,
this example uses a smaller number of larger bins; reducing the number of bins in
this way will not seriously affect the precision of ML estimates.
Berkson investigated the randomness of alpha-particle
emissions of Americium-241 (which has a half-life of about 458 years).
Physical theory suggests that, over a short period of time, the
interarrival times of observed particles would be independent and come
from an exponential distribution where the rate parameter is the mean
time between arrivals. The corresponding homogeneous Poisson process that
counts the number of emissions on the real-time line has arrival rate or
the intensity lambda=1/theta. The data consist of 10,220 observed interarrival
times of alpha particles (time unit equal to 1/5,000 second). The observed
interarrival times were put into intervals (or bins) running from 0 to 4,000
time units with interval lengths ranging from 25 to 100 time units, with one
additional interval for observed times exceeding 4,000 time units. To save space,
this example uses a smaller number of larger bins; reducing the number of bins in
this way will not seriously affect the precision of ML estimates.
Berkson investigated the randomness of alpha-particle
emissions of Americium-241 (which has a half-life of about 458 years).
Physical theory suggests that, over a short period of time, the
interarrival times of observed particles would be independent and come
from an exponential distribution where the rate parameter is the mean
time between arrivals. The corresponding homogeneous Poisson process that
counts the number of emissions on the real-time line has arrival rate or
the intensity lambda=1/theta. The data consist of 10,220 observed interarrival
times of alpha particles (time unit equal to 1/5,000 second). The observed
interarrival times were put into intervals (or bins) running from 0 to 4,000
time units with interval lengths ranging from 25 to 100 time units, with one
additional interval for observed times exceeding 4,000 time units. To save space,
this example uses a smaller number of larger bins; reducing the number of bins in
this way will not seriously affect the precision of ML estimates.
Berkson investigated the randomness of alpha-particle
emissions of Americium-241 (which has a half-life of about 458 years).
Physical theory suggests that, over a short period of time, the
interarrival times of observed particles would be independent and come
from an exponential distribution where the rate parameter is the mean
time between arrivals. The corresponding homogeneous Poisson process that
counts the number of emissions on the real-time line has arrival rate or
the intensity lambda=1/theta. The data consist of 10,220 observed interarrival
times of alpha particles (time unit equal to 1/5,000 second). The observed
interarrival times were put into intervals (or bins) running from 0 to 4,000
time units with interval lengths ranging from 25 to 100 time units, with one
additional interval for observed times exceeding 4,000 time units. To save space,
this example uses a smaller number of larger bins; reducing the number of bins in
this way will not seriously affect the precision of ML estimates.
Format
A data.frame with 8 rows and 4 variables:
[, 1] lower Start of an observation interval (in 1/5000 seconds) Numeric
[, 2] upper End of an observation interval (in 1/5000 seconds) Numeric
[, 3] event Event observed in the interval (right-censored/left-censored/interval-censored) Categoric
[, 4] count Number of events observed in the interval Numeric
A data.frame with 8 rows and 4 variables:
[, 1] lower Start of an observation interval (in 1/5000 seconds) Numeric
[, 2] upper End of an observation interval (in 1/5000 seconds) Numeric
[, 3] event Event observed in the interval (right-censored/left-censored/interval-censored) Categoric
[, 4] count Number of events observed in the interval Numeric
A data.frame with 8 rows and 4 variables:
[, 1] lower Start of an observation interval (in 1/5000 seconds) Numeric
[, 2] upper End of an observation interval (in 1/5000 seconds) Numeric
[, 3] event Event observed in the interval (right-censored/left-censored/interval-censored) Categoric
[, 4] count Number of events observed in the interval Numeric
A data.frame with 8 rows and 4 variables:
[, 1] lower Start of an observation interval (in 1/5000 seconds) Numeric
[, 2] upper End of an observation interval (in 1/5000 seconds) Numeric
[, 3] event Event observed in the interval (right-censored/left-censored/interval-censored) Categoric
[, 4] count Number of events observed in the interval Numeric
Source
Berkson, J. (1966), Examination of randomness of alpha-particle emissions,
in Festschrift for J. Neyman, Research Papers in Statistics, F. N. David, Editor,
New York, NY; John Wiley & Sons
Berkson, J. (1966), Examination of randomness of alpha-particle emissions,
in Festschrift for J. Neyman, Research Papers in Statistics, F. N. David, Editor,
New York, NY; John Wiley & Sons
Berkson, J. (1966), Examination of randomness of alpha-particle emissions,
in Festschrift for J. Neyman, Research Papers in Statistics, F. N. David, Editor,
New York, NY; John Wiley & Sons
Berkson, J. (1966), Examination of randomness of alpha-particle emissions,
in Festschrift for J. Neyman, Research Papers in Statistics, F. N. David, Editor,
New York, NY; John Wiley & Sons
Auburngrads/SMRD documentation built on Sept. 14, 2020, 2:21 a.m.
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Description
Berkson investigated the randomness of alpha-particle emissions of Americium-241 (which has a half-life of about 458 years). Physical theory suggests that, over a short period of time, the interarrival times of observed particles would be independent and come from an exponential distribution where the rate parameter is the mean time between arrivals. The corresponding homogeneous Poisson process that counts the number of emissions on the real-time line has arrival rate or the intensity lambda=1/theta. The data consist of 10,220 observed interarrival times of alpha particles (time unit equal to 1/5,000 second). The observed interarrival times were put into intervals (or bins) running from 0 to 4,000 time units with interval lengths ranging from 25 to 100 time units, with one additional interval for observed times exceeding 4,000 time units. To save space, this example uses a smaller number of larger bins; reducing the number of bins in this way will not seriously affect the precision of ML estimates.
Berkson investigated the randomness of alpha-particle emissions of Americium-241 (which has a half-life of about 458 years). Physical theory suggests that, over a short period of time, the interarrival times of observed particles would be independent and come from an exponential distribution where the rate parameter is the mean time between arrivals. The corresponding homogeneous Poisson process that counts the number of emissions on the real-time line has arrival rate or the intensity lambda=1/theta. The data consist of 10,220 observed interarrival times of alpha particles (time unit equal to 1/5,000 second). The observed interarrival times were put into intervals (or bins) running from 0 to 4,000 time units with interval lengths ranging from 25 to 100 time units, with one additional interval for observed times exceeding 4,000 time units. To save space, this example uses a smaller number of larger bins; reducing the number of bins in this way will not seriously affect the precision of ML estimates.
Berkson investigated the randomness of alpha-particle emissions of Americium-241 (which has a half-life of about 458 years). Physical theory suggests that, over a short period of time, the interarrival times of observed particles would be independent and come from an exponential distribution where the rate parameter is the mean time between arrivals. The corresponding homogeneous Poisson process that counts the number of emissions on the real-time line has arrival rate or the intensity lambda=1/theta. The data consist of 10,220 observed interarrival times of alpha particles (time unit equal to 1/5,000 second). The observed interarrival times were put into intervals (or bins) running from 0 to 4,000 time units with interval lengths ranging from 25 to 100 time units, with one additional interval for observed times exceeding 4,000 time units. To save space, this example uses a smaller number of larger bins; reducing the number of bins in this way will not seriously affect the precision of ML estimates.
Berkson investigated the randomness of alpha-particle emissions of Americium-241 (which has a half-life of about 458 years). Physical theory suggests that, over a short period of time, the interarrival times of observed particles would be independent and come from an exponential distribution where the rate parameter is the mean time between arrivals. The corresponding homogeneous Poisson process that counts the number of emissions on the real-time line has arrival rate or the intensity lambda=1/theta. The data consist of 10,220 observed interarrival times of alpha particles (time unit equal to 1/5,000 second). The observed interarrival times were put into intervals (or bins) running from 0 to 4,000 time units with interval lengths ranging from 25 to 100 time units, with one additional interval for observed times exceeding 4,000 time units. To save space, this example uses a smaller number of larger bins; reducing the number of bins in this way will not seriously affect the precision of ML estimates.
Format
A data.frame with 8 rows and 4 variables:
| [, 1] | lower | Start of an observation interval (in 1/5000 seconds) | Numeric |
| [, 2] | upper | End of an observation interval (in 1/5000 seconds) | Numeric |
| [, 3] | event | Event observed in the interval (right-censored/left-censored/interval-censored) | Categoric |
| [, 4] | count | Number of events observed in the interval | Numeric |
A data.frame with 8 rows and 4 variables:
| [, 1] | lower | Start of an observation interval (in 1/5000 seconds) | Numeric |
| [, 2] | upper | End of an observation interval (in 1/5000 seconds) | Numeric |
| [, 3] | event | Event observed in the interval (right-censored/left-censored/interval-censored) | Categoric |
| [, 4] | count | Number of events observed in the interval | Numeric |
A data.frame with 8 rows and 4 variables:
| [, 1] | lower | Start of an observation interval (in 1/5000 seconds) | Numeric |
| [, 2] | upper | End of an observation interval (in 1/5000 seconds) | Numeric |
| [, 3] | event | Event observed in the interval (right-censored/left-censored/interval-censored) | Categoric |
| [, 4] | count | Number of events observed in the interval | Numeric |
A data.frame with 8 rows and 4 variables:
| [, 1] | lower | Start of an observation interval (in 1/5000 seconds) | Numeric |
| [, 2] | upper | End of an observation interval (in 1/5000 seconds) | Numeric |
| [, 3] | event | Event observed in the interval (right-censored/left-censored/interval-censored) | Categoric |
| [, 4] | count | Number of events observed in the interval | Numeric |
Source
Berkson, J. (1966), Examination of randomness of alpha-particle emissions, in Festschrift for J. Neyman, Research Papers in Statistics, F. N. David, Editor, New York, NY; John Wiley & Sons
Berkson, J. (1966), Examination of randomness of alpha-particle emissions, in Festschrift for J. Neyman, Research Papers in Statistics, F. N. David, Editor, New York, NY; John Wiley & Sons
Berkson, J. (1966), Examination of randomness of alpha-particle emissions, in Festschrift for J. Neyman, Research Papers in Statistics, F. N. David, Editor, New York, NY; John Wiley & Sons
Berkson, J. (1966), Examination of randomness of alpha-particle emissions, in Festschrift for J. Neyman, Research Papers in Statistics, F. N. David, Editor, New York, NY; John Wiley & Sons
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