Mehdi Hosseinkouchack

Estimating the parameters of Weibull distribution using simulated annealing algorithm

Weibull distribution plays an important role in failure distribution modeling in reliability studies. It is a hard work to estimate the parameters of Weibull distribution. This distribution has three parameters, but for simplicity, a parameter is omitted and as a result, the estimation of the others will be easily done. When the three-parameter distribution is of interest, the estimation procedure will be quite boring. Maximum likelihood estimation is a good method, which is usually used to elaborate on the parameter estimation. The likelihood function formed for the parameter estimation of a three-parameter Weibull distribution is very hard to maximize. Many researchers have studied this maximization problem. In this paper, we have briefly discussed this problem and proposed a new approach based on the simulated algorithm to solve that.

Estimating parameters of the three-parameter Weibull distribution using a neural network

Weibull distributions play an important role in reliability studies and have many applications in engineering. It normally appears in the statistical scripts as having two parameters, making it easy to estimate its parameters. However, once you go beyond the two parameter distribution, things become complicated. For example, estimating the parameters of a three-parameter Weibull distribution has historically been a complicated and sometimes contentious line of research since classical estimation procedures such as Maximum Likelihood Estimation (MLE) have become almost too complicated to implement. In this paper, we will discuss an approach that takes advantage of Artificial Neural Networks (ANN), which allow us to propose a simple neural network that simultaneously estimates the three parameters. The ANN neural network exploits the concept of the moment method to estimate Weibull parameters using mean, standard deviation, median, skewness and kurtosis. To demonstrate the power of the proposed ANN-based method we conduct an extensive simulation study and compare the results of the proposed method with an MLE and two moment-based methods. [Submitted 23 September 2007; Revised 11 December 2007; Second revision 22 December 2007; Accepted 10 January 2008]

The Local Power of the CADF and CIPS Panel Unit Root Tests

Very little is known about the local power of second generation panel unit root tests that are robust to cross-section dependence. This article derives the local asymptotic power functions of the cross-section argumented Dickey–Fuller Cross-section Augmented Dickey-Fuller (CADF) and CIPS tests of Pesaran (2007), which are among the most popular tests around.

Global Financial Transmission into Sub-Saharan Africa – A Global Vector Autoregression Analysis

Sub-Saharan African countries are exposed to spillovers from global financial variables, but the impact on economic activity is more significant in more financially developed economies. Generalized impulse responses from a GVAR exercise demonstrate how the CBOE volatility index (VIX) and credit conditions around the globe impact a subset of sub-Saharan African economies and regions. The estimated relationships suggest that the effect of global uncertainty is more pervasive in exports, with the impact on economic and lending activities being mixed. The channels of transmission include the effects of global financial variables on commodity prices and on trading-partner’s macroeconomic and financial variables. The analysis suggests that shocks to credit conditions in the euro area and the U.S. have not significantly affected local lending conditions or economic activity in sub-Saharan Africa during 1991-2011, except perhaps in South Africa.

Ratio Tests under Limiting Normality

We propose a class of ratio tests that is applicable whenever a cumulation (of transformed) data is asymptotically normal upon appropriate normalization. All it requires is the orthonormal expansion using the Karhunen-Loeve [KL] theorem, which is employed to compute weighted averages of the data. The test statistics are ratios of quadratic forms of these averages, and hence turn out to be scale-invariant by construction: The scaling parameter cancels asymptotically without having to be estimated. Limiting distributions are obtained. Critical values and asymptotic local power functions can be calculated by means of standard numerical means. The method to construct such ratio tests is illustrated with three limiting normal cases (Brownian motion, Brownian bridge, and Ornstein-Uhlenbeck process), which are applicable in many empirical situations. The ratio tests are directed against local alternatives and turn out to be almost as powerful as optimal competitors.

Modified CADF and CIPS Panel Unit Root Statistics with Standard Chi-squared and Normal Limiting Distributions

In an influential paper Pesaran (‘A simple panel unit root test in presence of cross-section dependence’, Journal of Applied Econometrics, Vol. 22, pp. 265–312, 2007) proposes two unit root tests for panels with a common factor structure. These are the CADF and CIPS test statistics, which are amongst the most popular test statistics in the literature. One feature of these statistics is that their limiting distributions are highly non-standard, making for relatively complicated implementation. In this paper, we take this feature as our starting point to develop modified CADF and CIPS test statistics that support standard chi-squared and normal inference.

Powerful Unit Root Tests Free of Nuisance Parameters

We propose a variance ratio‐type unit root test where the nuisance parameter cancels asymptotically under both the null of a unit root and a local‐to‐unity alternative. Critical values and asymptotic power curves can be computed using standard numerical techniques. Our test exhibits higher power compared with tests that share the virtue of being free of tuning parameters. In fact, the local asymptotic power curves of our procedure get close to the power functions of the point optimal test, where the latter suffers from the drawback of having to correct for a nuisance parameter consistently.

Harmonically Weighted Processes: The Case of U.S. Inflation

We suggest a model for long memory in time series that amounts to harmonically weighting short memory processes, ∑ j x t − j / ( j 1). A nonstandard rate of convergence is required to establish a Gaussian functional central limit theorem. Further, we study the asymptotic least squares theory when harmonically weighted processes are regressed on each other. The regression estimators converge to Gaussian limits upon the conventional normalization with square root of the sample size, and standard testing procedures apply. Harmonically weighted processes do not allow - or require - to choose a memory parameter. Nevertheless, they may well be able to capture dynamics that have been modelled by fractional integration in the past, and the conceptual simplicity of the new model may turn out to be a worthwhile advantage in practice. The harmonic inverse transformation that removes this kind of long memory is also developed. We successfully apply the procedure to monthly U.S. inflation, and provide simulation evidence that fractional integration of order d is well captured by harmonic weighting over a relevant range of d in finite samples.

Panel Cointegration Testing in the Presence of Linear Time Trends

We consider a class of panel tests of the null hypothesis of no cointegration and cointegration. All tests under investigation rely on single-equations estimated by least squares, and they may be residual-based or not. We focus on test statistics computed from regressions with intercept only (i.e., without detrending) and with at least one of the regressors (integrated of order 1) being dominated by a linear time trend. In such a setting, often encountered in practice, the limiting distributions and critical values provided for and applied with the situation “with intercept only” are not correct. It is demonstrated that their usage results in size distortions growing with the panel size N . Moreover, we show which are the appropriate distributions, and how correct critical values can be obtained from the literature.

Distribution of the Durbin–Watson Statistic in Near Integrated Processes

This paper analyzes the Durbin–Watson (DW) statistic for near-integrated processes. Using the Fredholm approach the limiting characteristic function of DW is derived, in particular focusing on the effect of a “large initial condition” growing with the sample size. Random and deterministic initial conditions are distinguished. We document the asymptotic local power of DW when testing for integration.