STATISTICAL APPROACH FOR OPEN BONUS MALUS

2013 ◽  
Vol 44 (1) ◽  
pp. 63-83 ◽  
Author(s):  
Gracinda Rita Guerreiro ◽  
João Tiago Mexia ◽  
Maria de Fátima Miguens
Keyword(s):  
Statistical Approach ◽  
Confidence Regions ◽  
Numerical Results ◽  
Asymptotic Distributions ◽  
Expected Number ◽  
System Evolution ◽  
Portfolio Approach ◽  
New Policies

AbstractIn this paper, following an open portfolio approach, we show how to estimate a Bonus-malus system evolution.Considering a model for the number of new annual policies, we obtain ML estimators, asymptotic distributions and confidence regions for the expected number of new policies entering the portfolio in each year, as well as for the expected number and proportion of insureds in each bonus class, by year of enrollment. Confidence regions for the distribution of policyholders result in confidence regions for optimal bonus scales.Our treatment is illustrated by an example with numerical results.

scholarly journals A Statistical Investigation of Prominence Fine Structure in the EUV

1998 ◽  
Vol 167 ◽  
pp. 59-62
Author(s):  
S. Pojoga ◽  
A.G. Nikoghossian ◽  
Z. Mouradian
Keyword(s):  
Fine Structure ◽  
Statistical Approach ◽  
Statistical Investigation ◽  
Structural Elements ◽  
Expected Number

AbstractA statistical approach is proposed for the study of the prominence fine structure. Intensity variations in several EUV lines are measured in different regions of prominences. The expected number of fine structural elements is derived.

scholarly journals Modified Variance Ratio Test for Autocorrelation in the Presence of Heteroskedasticity

2018 ◽  
Vol 23 (1) ◽  
pp. 1-19
Author(s):  
Sohail Chand ◽  
Nuzhat Aftab
Keyword(s):  
Stock Exchange ◽  
Numerical Results ◽  
Asymptotic Distributions ◽  
Small Samples ◽  
Ratio Test ◽  
Variance Ratio ◽  
Variance Ratio Test ◽  
Daily Returns

Given that autocorrelation tests do not perform well in the presence of heteroskedasticity and in variance-break cases, we present three modified weighted variance ratio tests of autocorrelation. The numerical results show that the proposed tests perform better for small samples. They provide a better approximation of asymptotic distributions and are more powerful when the lag length is mis-specified. The study also applies these tests to data on the daily returns of two companies listed on the Pakistan Stock Exchange.

scholarly journals On the Expected Number of Limited Length Binary Strings Derived by Certain Urn Models

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Frosso S. Makri ◽  
Zaharias M. Psillakis
Keyword(s):  
Stochastic Processes ◽  
Numerical Results ◽  
Urn Models ◽  
Urn Model ◽  
Critical Events ◽  
Expected Number ◽  
Limited Length ◽  
Binary Strings

The expected number of 0-1 strings of a limited length is a potentially useful index of the behavior of stochastic processes describing the occurrence of critical events (e.g., records, extremes, and exceedances). Such model sequences might be derived by a Hoppe-Polya or a Polya-Eggenberger urn model interpreting the drawings of white balls as occurrences of critical events. Numerical results, concerning average numbers of constrained length interruptions of records as well as how on the average subsequent exceedances are separated, demonstrate further certain urn models.

Suicide in prisons

1999 ◽  
Vol 175 (1) ◽  
pp. 50-55 ◽  
Author(s):  
Sheila M. Gore
Keyword(s):  
Opioid Dependence ◽  
Statistical Approach ◽  
Expected Number ◽  
England And Wales ◽  
Gender And Age ◽  
High Prevalence ◽  
Age Appropriate ◽  
And Gender ◽  
Opioid Users ◽  
Number Of Individuals

BackgroundA recent review showed that opioid users' deaths from suicide were 10 times as common as expected on the basis of age and gender. Surveys showing prisoners' high prevalence of injecting or opioid dependence have led to a new statistical approach to prison suicides.AimsTo estimate the expected number of UK prison suicides annually, having taken account of inmates' age, gender and opioid dependence.MethodBy gender, estimate the effective number of individuals (in terms of community-equivalent suicide risk) for whom prisons have a duty of care as 10 times the number of opioid-dependent inmates plus the number of non-opioid user inmates. Apply the gender and age-appropriate national suicide rates to work out the expected number of prison suicides.ResultsThe Scottish Prison Service can expect 7.1 suicides per annum, and annual totals up to 12 without exacerbation of suicides due to incarceration. For the Prison Service in England and Wales, 19.3 suicides per annum can be expected in prisons, and annual totals may range up to 28 without indicating incarceration; the total of self-inflicted deaths was 47 in 1993–94ConclusionsPrisons cannot prevent all suicides. An alert may be warranted if prison suicides exceed 12 per annum in Scotland, or 28 in England and Wales.

OPTIMAL INSPECTION ORDER WHEN PROCESS’ FAILURE RATE IS CONSTANT

1996 ◽  
Vol 03 (01) ◽  
pp. 25-41 ◽  
Author(s):  
QI-MING HE ◽  
YIGAL GERCHAK ◽  
ABRAHAM GROSFELD-NIR
Keyword(s):  
Failure Rate ◽  
Optimal Policy ◽  
A Priori ◽  
Numerical Results ◽  
Expected Number ◽  
Process Failure ◽  
Inspection Policy

Suppose that a lot has been produced by a process with a constant failure rate. So either the entire lot is good, or all units up to some point are good and from that point on are all defective. We wish to determine the order in which units in such lot should be inspected so as to minimize the expected number of inspections needed to identify all defectives. Unlike previous work in this area, we do not a priori assume that the last unit in the lot is defective, and that key difference turns out to dramatically influence the nature of the optimal inspection policy and the expected number of units inspected. After analyzing the optimal policy, we suggest a very simple and intuitive heuristic, which turns out to perform extremely well. Numerical results are provided.

The probabilities of rooted tree-shapes generated by random bifurcation

1971 ◽  
Vol 3 (01) ◽  
pp. 44-77 ◽  
Author(s):  
E. F. Harding
Keyword(s):  
Probability Distribution ◽  
Statistical Approach ◽  
Rooted Tree ◽  
Difficult Problem ◽  
Numerical Results ◽  
Rooted Trees ◽  
Evolutionary Trees ◽  
Mathematical Problems ◽  
Labelled Trees ◽  
Random Bifurcation

The set of rooted trees, generated by random bifurcation at the terminal nodes, is considered with the aims of enumerating it and of determining its probability distribution. The account of enumeration collates much previous work and attempts a complete perspective of the problems and their solutions. Asymptotic and numerical results are given, and some unsolved problems are pointed out. The problem of ascertaining the probability distribution is solved by obtaining its governing recurrence equation, and numerical results are given. The difficult problem of determining the most probable tree-shape of given size is considered, and for labelled trees a conjecture at its solution is offered. For unlabelled shapes the problem remains open. These mathematical problems arise in attempting to reconstruct evolutionary trees by the statistical approach of Cavalli-Sforza and Edwards.

scholarly journals Prediction of the amplitude of solar cycle 25 using polar faculae observations

2020 ◽  
Author(s):  
Jan Janssens
Keyword(s):  
Solar Cycle ◽  
Sunspot Number ◽  
Solar Flares ◽  
Solar Disk ◽  
Statistical Approach ◽  
Expected Number ◽  
Heliographic Latitude ◽  
Cycle Minimum ◽  
Commercial Off The Shelf ◽  
Cassegrain Telescope

Aims . Based on the monthly number of polar faculae, a forecast of the amplitude of solar cycle 25 (SC25) is provided, as well as a prediction of the number of solar flares. Methods . Faculae near both solar poles have been visually observed using a commercial off-the-shelf 20 cm Schmidt-Cassegrain telescope since 1995. The monthly averages were corrected for varying seeing conditions and the heliographic latitude of the center of the solar disk B 0 . From the deduced relationship between the smoothed number of monthly polar faculae during the solar cycle minimum, and the subsequent maximum of the monthly sunspot number, a prediction has been made for the amplitude of the next solar cycle. The methodology used can be considered as a precursor technique. The expected number of M- and X-class flares was calculated based on a statistical approach. Results. The maximum of SC25 is predicted to be 118 +/- 29, of similar strength than the previous SC24. Also the number of M5 or stronger flares is expected to be comparable to that of the previous solar cycle.

The probabilities of rooted tree-shapes generated by random bifurcation

1971 ◽  
Vol 3 (1) ◽  
pp. 44-77 ◽  
Author(s):  
E. F. Harding
Keyword(s):  
Probability Distribution ◽  
Statistical Approach ◽  
Rooted Tree ◽  
Difficult Problem ◽  
Numerical Results ◽  
Rooted Trees ◽  
Evolutionary Trees ◽  
Mathematical Problems ◽  
Labelled Trees ◽  
Random Bifurcation

The set of rooted trees, generated by random bifurcation at the terminal nodes, is considered with the aims of enumerating it and of determining its probability distribution. The account of enumeration collates much previous work and attempts a complete perspective of the problems and their solutions. Asymptotic and numerical results are given, and some unsolved problems are pointed out. The problem of ascertaining the probability distribution is solved by obtaining its governing recurrence equation, and numerical results are given. The difficult problem of determining the most probable tree-shape of given size is considered, and for labelled trees a conjecture at its solution is offered. For unlabelled shapes the problem remains open. These mathematical problems arise in attempting to reconstruct evolutionary trees by the statistical approach of Cavalli-Sforza and Edwards.

A Co-Ordinated System of Calculations for Altered Policies

1973 ◽  
Vol 34 ◽  
pp. 49-123
Author(s):  
G. G. Torkington
Keyword(s):  
Numerical Results ◽  
Computer Application ◽  
Clerical Staff ◽  
Conventional Methods ◽  
Premium Rates ◽  
New Policies ◽  
Skilled Staff ◽  
Selection Of

SynopsisThis paper describes a practical co-ordinated system of calculating financial terms for policy alterations and calculating surrender and paid-up values of policies which have been altered. The system is primarily designed to produce numerical results which are consistent, equitable and capable of evaluation without the need for special actuarial experience. The calculation formulae make use of the tabular rates of surrender values and paid-up values currently granted for unaltered policies and the current premium rates charged for new policies; the often difficult selection of suitable actuarial functions is thereby avoided automatically without departing from general actuarial principles. Since the actuarial bases inherent in these tabular rates are not used explicitly the rates can be changed independently at any time without affecting the use of the formulae. The system is equally suitable for operation by clerical staff or for computer application and should produce economies in the valuable time of skilled staff.At the end of the paper, examples are given comparing results with those calculated by conventional methods.

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