1
1726-4057
Iranian Statistical Society
291
On Orthogonalization Approach to Construct a Multiple Input Transfer Function Model
Khalaﬁ
Mahnaz
Azimmohseni
Majid
Kordkatuli
Mohammad
1
12
2014
13
2
135
150
16
12
2014
16
12
2014
In this article, a special type of orthogonalization is obtained to construct a multiple input transfer function model. By using this technique, construction of a transfer function model is divided to sequential construction of transfer function models with less input time series. Furthermore, based on real and simulated time series we provide an instruction to adequately perform the stages of orthogonalization algorithm.
292
Estimation and Reconstruction Based on Left Censored Data from Pareto Model
Asgharzadeh
A.
Mohammadpour
M.
Ganji
Z. M.
1
12
2014
13
2
151
175
16
12
2014
16
12
2014
In this paper, based on a left censored data from the twoparameter Pareto distribution, maximum likelihood and Bayes estimators for the two unknown parameters are obtained. The problem of reconstruction of the past failure times, either point or interval, in the left-censored set-up, is also considered from Bayesian and non-Bayesian approaches. Two numerical examples and a Monte Carlo simulation study are given for illustrative purposes.
293
Karlin’s Basic Composition Theorems and Stochastic Orderings
Khaledi
Baha-Eldin
1
12
2014
13
2
177
186
16
12
2014
16
12
2014
Suppose λ,x,ζ traverse the ordered sets Λ, X and Z, respectively and consider the functions f(λ,x,ζ) and g(λ,ζ) satisfying the following conditions,
(a) f(λ,x,ζ) > 0 and f is TP2 in each pairs of variables when the third variable is held ﬁxed and
(b) g(λ,ζ) is TP2.
Then the function
h(λ,x) =∫Z f(λ,x,ζ)g(λ,ζ)dµ(ζ), deﬁned on Λ×X is TP2 in (λ,x). The aim of this note is to use a new stochastic ordering argument to prove the above result and simplify it’s proof given by Karlin (1968). We also prove some other new versions of this result.
294
Tracking Interval for Type II Hybrid Censoring Scheme
Panahi
H.
Sayyareh
A.
1
12
2014
13
2
187
208
16
12
2014
16
12
2014
The purpose of this paper is to obtain the tracking interval for diﬀerence of expected Kullback-Leibler risks of two models under Type II hybrid censoring scheme. This interval helps us to evaluate proposed models in comparison with each other. We drive a statistic which tracks the diﬀerence of expected Kullback–Leibler risks between maximum likelihood estimators of the distribution in two diﬀerent models and obtain an estimator of the variance of this statistic under Type II hybrid censoring scheme. Monte Carlo simulations are performed to verify the theoretical results. A real data set representing micro-droplet splashing reported in 90◦ spray angle is used to illustrate the results for the tracking interval. Furthermore, because of the great importance of prediction in coating industries, pivotal method is considered to obtain the prediction interval of future observation of the droplet splashing based on Type II hybrid censored sample.
295
A New Class of Zero-Inﬂated Logarithmic Series Distribution
Satheesh Kumar
C.
Riyaz
A.
1
12
2014
13
2
209
224
16
12
2014
16
12
2014
Through this paper we suggest an alternative form of the modiﬁed zero-inﬂated logarithmic series distribution of Kumar and Riyaz (Statistica, 2013) and study some of its important aspects. The method of maximum likelihood is employed for estimating the parameters of the distribution and certain test procedures are considered for testing the signiﬁcance of the additional parameter of the model. Further, all the procedures are illustrated with the help of two real life data sets.
296
Economic Design of T2 −V SSC Chart Using Genetic Algorithms
Arbabi
Marzieh
Rezaei Ghahroodi
Zahra
1
12
2014
13
2
225
247
16
12
2014
16
12
2014
The principal function of a control chart is to help management distinguish diﬀerent sources of variation in a process. Control charts are widely used as a graphical tool to monitor a process in order to improve the quality of the product. Chen and Hsieh (2007) have designed a T2 control chart using a Variable Sampling Size and Control limits (V SSC) scheme. They have shown that using the V SSC scheme results in charts with more statistical power to detect small to moderate shifts in the process mean vector than the other T2 charts. In this paper, we develop an economic design for the T2 −V SSC chart to help determine the design parameters and then minimize the cost model proposed by Costa and Rahim (2001) using a Genetic Algorithm (GA) approach. We also compare economic design of the T2 −V SSC chart with the T2 −DWL, T2 −V SSI and T2 −FRS charts so as to choose the best option and, ﬁnally, carry out a sensitivity analysis to investigate the eﬀects of model parameters on the solution of the economic design.