The estimation of a location parameter when the scale parameter is confined to a finite range: The notion of a generalized ancillary statistic

Biometrika ◽  
1989 ◽  
Vol 76 (3) ◽  
pp. 609-612 ◽  
Author(s):  
S. R. CHAMBERLIN ◽  
D. A. SPROTT
Keyword(s):  
Scale Parameter ◽  
Location Parameter ◽  
Finite Range ◽  
Ancillary Statistic

scholarly journals Sequential point and interval estimation of scale parameter of exponential distribution

1995 ◽  
Vol 18 (2) ◽  
pp. 383-390
Author(s):  
Z. Govindarajulu
Keyword(s):  
Exponential Distribution ◽  
Scale Parameter ◽  
Stopping Time ◽  
Interval Estimation ◽  
Location Parameter ◽  
Exact Expression ◽  
Point Estimation ◽  
Quadratic Loss ◽  
Negative Exponential Distribution ◽  
Negative Exponential

Sequential fixed-width confidence intervals are obtained for the scale parameterσwhen the location parameterθof the negative exponential distribution is unknown. Exact expressions for the stopping time and the confidence coefficient associated with the sequential fixed-width interval are derived. Also derived is the exact expression for the stopping time of sequential point estimation with quadratic loss and linear cost. These are numerically evaluated for certain nominal confidence coefficients, widths of the interval and cost functions, and are compared with the second order asymptotic expressions.

scholarly journals Modelling non-stationary annual maximum flood heights in the lower Limpopo River basin of Mozambique

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
Daniel Maposa ◽  
James J. Cochran ◽  
Maseka Lesaoana
Keyword(s):  
River Basin ◽  
Scale Parameter ◽  
Linear Trend ◽  
Location Parameter ◽  
Extreme Value ◽  
Time Dependent ◽  
Sufficient Evidence ◽  
Annual Maximum ◽  
Significant Linear Trend ◽  
Gev Distribution

In this article we fit a time-dependent generalised extreme value (GEV) distribution to annual maximum flood heights at three sites: Chokwe, Sicacate and Combomune in the lower Limpopo River basin of Mozambique. A GEV distribution is fitted to six annual maximum time series models at each site, namely: annual daily maximum (AM1), annual 2-day maximum (AM2), annual 5-day maximum (AM5), annual 7-day maximum (AM7), annual 10-day maximum (AM10) and annual 30-day maximum (AM30). Non-stationary time-dependent GEV models with a linear trend in location and scale parameters are considered in this study. The results show lack of sufficient evidence to indicate a linear trend in the location parameter at all three sites. On the other hand, the findings in this study reveal strong evidence of the existence of a linear trend in the scale parameter at Combomune and Sicacate, whilst the scale parameter had no significant linear trend at Chokwe. Further investigation in this study also reveals that the location parameter at Sicacate can be modelled by a nonlinear quadratic trend; however, the complexity of the overall model is not worthwhile in fit over a time-homogeneous model. This study shows the importance of extending the time-homogeneous GEV model to incorporate climate change factors such as trend in the lower Limpopo River basin, particularly in this era of global warming and a changing climate.Keywords: nonstationary extremes; annual maxima; lower Limpopo River; generalised extreme value

scholarly journals Impact of Dependence on Parameter Estimates of Autoregressive Process with Gumbel Distributed Innovation

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 365-380
Author(s):  
Sunday Samuel Bako ◽  
Mohd Bakri Adam ◽  
Anwar Fitrianto
Keyword(s):  
Scale Parameter ◽  
Extreme Values ◽  
Real Life ◽  
Location Parameter ◽  
Autoregressive Process ◽  
Parameter Estimates ◽  
Distributed Data ◽  
Original Series ◽  
Real Life Data ◽  
Ar Process

Recent studies have shown that independent identical distributed Gaussian random variables is not suitable for modelling extreme values observed during extremal events. However, many real life data on extreme values are dependent and stationary rather than the conventional independent identically distributed data. We propose a stationary autoregressive (AR) process with Gumbel distributed innovation and characterise the short-term dependence among maxima of an (AR) process over a range of sample sizes with varying degrees of dependence. We estimate the maximum likelihood of the parameters of the Gumbel AR process and its residuals, and evaluate the performance of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto (GPD) distribution and we evaluate the performance of the parameter estimates fitted to the cluster maxima and the original series. Ignoring the effect of dependence leads to overestimation of the location parameter of the Gumbel-AR (1) process. The estimate of the location parameter of the AR process using the residuals gives a better estimate. Estimate of the scale parameter perform marginally better for the original series than the residual estimate. The degree of clustering increases as dependence is enhance for the AR process. The Gumbel-AR(1) fitted to the Gumbel-GPD shows that the estimates of the scale and shape parameters fitted to the cluster maxima perform better as sample size increases, however, ignoring the effect of dependence lead to an underestimation of the parameter estimates of the scale parameter. The shape parameter of the original series gives a superior estimate compare to the threshold excesses fitted to the Gumbel-GPD.

Sign in / Sign up

Export Citation Format

Share Document