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The inverse Gaussian distribution arises quite naturally as a model for failure times brought on by a “steady” deterioration in quality. If the underlying “wear” process is one of Brownian motion with a positive drift at rate µ, with variance σ2 per unit time, the first passage time T to a barrier at a distance a from the origin has p.d.f. of inverse Gaussian type.

The development of digital technology has provided technical support to various industries. Specifically, Internet-based freight platforms can ensure the high-quality development of the logistics industry. Online freight platforms can use cargo transportation insurance to improve their service capabilities, promote their differentiated development, create products with platform characteristics and increase their core competitiveness.

This study uses a generalised linear model to fit the claim probability and claim intensity data and analyses freight insurance pricing based on the freight insurance claim data of a freight platform in China.

Considering traditional pricing risk factors, this study adds two risk factors to fit the claim probability data, that is, the purchase behaviour of freight insurance customers and road density. The two variables can significantly influence the claim probability, and the model fitting outcomes obtained with the logit connection function are excellent. In addition, this study examines the model results under various distribution types for the fitting of the claim intensity data. The fitting outcomes under a gamma distribution are superior to those under the other distribution types, as measured by the Akaike information criterion.

With actual data from an online freight platform in China, this study empirically proves that a generalised linear model is superior to traditional pricing methods for freight insurance. This study constructs a generalised linear pricing model considering the unique features of the freight industry and determines that the transportation distance, cargo weight and road density have a significant influence on the claim probability and claim intensity.

Cyber risk refers to risk affecting information and technology assets of a corporation or government institution. As cyber risk management become important, insurance is one possible solution. However, lack of data and severe information asymmetries increase the difficulties in pricing-related insurance products. In this chapter, we discuss first-party insurance that indemnifies the loss when the insured encounters virus attack and provide pricing model for the policy using copula methodology. Simulation results show that model risk may exist in the distribution of server downtime hours and is minor in the distribution of incident frequency and number of personal computers (PCs) infected.

Acceptance sampling can be both time‐consuming and destructive so that it is desirable to arrive at a sound lot disposition decision in a timely manner. Sequential sampling plans are attractive since they offer a lower average sample number than do matched single, double, or multiple sampling plans. Analogously, cumulative sum control charts offer the ability to detect moderate process shifts more rapidly than do Shewhart control charts applied to the same process. The inverse Gaussian distribution is flexible and is often the model of choice in accelerated life testing applications where early failure times predominate. Based on sequential probability ratio tests (SPRT), sequential sampling/ cumulative sum (CUSUM) plans provide timely, statistically based decisions. Presents SPRT and CUSUM results for the inverse Gaussian process mean. Also presents a simple goodness‐of‐fit test for the inverse Gaussian distribution which allows for model adequacy checking.

The purpose of this study is to describe precisely the wind speed regime and characteristics of a runway of an International Airport, the north-western part of Turkey.

Three different probability distributions, namely, Inverse Gaussian (IG), widely used two-parameter Weibull and Rayleigh distributions in the literature, are used to represent wind regime and characteristics of the runway. The parameters of each distribution are estimated by the pattern search (PS)-based heuristic algorithm. The results are compared with the other three methods-based numerical computation, including maximum-likelihood method, moment method (MoM) and power density method, respectively. To evaluate the fitting performance of the proposed method, several statistical goodness tests including the mostly used root mean square error (RMSE) and chi-squared (X²) are conducted.

In the light of the statistical goodness tests, the results of the IG-based PS attain better performance than the classical Weibull and Rayleigh functions. Both the RMSE and X² values achieved by the IG-based PS method lower than that of Weibull and Rayleigh distributions. It exhibits a better fitting performance with 0.0074 for RMSE and 0.58 × 10⁻⁴ for X² for probability density function (PDF) in 2012 and with RMSE of 0.0084 and X² of 0.74 × 10⁻⁴ for PDF in 2013. As regard the cumulative density function of the measured wind data, the best results are found to be Weibull-based PS with RMSE of 0.0175 and X² of 3.25 × 10⁻⁴ in 2012. However, Weibull-based MoM shows more excellent ability in 2013, with RMSE of 0.0166 and X² of 2.94 × 10⁻⁴. Consequently, it is considered that the results of this study confirm that IG-based PS with the lowest error value can a good choice to model more accurately and characterize the wind speed profile of the airport.

This paper presents a realistic point of view regarding the wind regime and characteristics of an airport. This study may cast the light on researchers, policymakers, policy analysts and airport designers intending to investigate the wind profile of a runway at the airport in the world and also provide a significant pathway on how to determine the wind distribution of the runway.

Instead of the well-known Weibull distribution for the representing of wind distribution in the literature, in this paper, IG distribution is used. Furthermore, the suitability of IG to represent the wind distribution is validated when compared with two-parameter Weibull and Rayleigh distributions. Besides, the performance and efficiency of PS have been evaluated by comparing it with other methods.

Distributions of index terms have been used in modelling information retrieval systems and databases. Most previous models used some form of the Zipf distribution. This work uses a probability model of the occurrence of index terms to derive discrete distributions which are mixtures of Poisson and negative binomial distributions. These distributions, the generalised inverse Gaussian‐Poisson and the Generalised Waring give better fits than the simpler Zipf distribution, particularly in the tails of the distribution where the high frequency terms are found. They have the advantage of being more explanatory and can incorporate a time parameter if necessary.

This article considers Inverse Gaussian distribution as the basic lifetime model for the test units. The unknown model parameters are estimated using the method of moments, the method of maximum likelihood and Bayesian methods. As part of maximum likelihood analysis, this article employs an expectation-maximization algorithm to simplify numerical computation. Subsequently, Bayesian estimates are obtained using the Metropolis–Hastings algorithm. This article then presents the design of optimal censoring schemes using a design criterion that deals with the precision of a particular system lifetime quantile. The optimal censoring schemes are obtained after taking into account budget constraints.

This article first presents classical and Bayesian statistical inference for Progressive Type-I Interval censored data. Subsequently, this article considers the design of optimal Progressive Type-I Interval censoring schemes after incorporating budget constraints.

A real dataset is analyzed to demonstrate the methods developed in this article. The adequacy of the lifetime model is ensured using a simulation-based goodness-of-fit test. Furthermore, the performance of various estimators is studied using a detailed simulation experiment. It is observed that the maximum likelihood estimator relatively outperforms the method of moment estimator. Furthermore, the posterior median fares better among Bayesian estimators even in the absence of any subjective information. Furthermore, it is observed that the budget constraints have real implications on the optimal design of censoring schemes.

The proposed methodology may be used for analyzing any Progressive Type-I Interval Censored data for any lifetime model. The methodology adopted to obtain the optimal censoring schemes may be particularly useful for reliability engineers in real-life applications.

Ajiferuke showed that observed author distributions can best be described by a shifted inverse Gaussian‐Poisson distribution. Yet, in the framework of a model to explain observed fractional distributions of authors it is important to know whether a simple one‐parameter distribution such as a geometric or a truncated Poisson can adequately describe observed author distributions, at least in those fields where the single author is still dominant. In this article it is shown that for the field of information science this is indeed the case.

This article describes reliability analysis and failure cause determination in encapsulated semiconductor devices. Such devices were subjected to a destructive life test using temperature as an accelerating stress. Once the devices had failed, the failure data were statistically analysed with the aid of a digital computer. The failed devices were then decapsulated and failure causes were determined using different types of microscopy. The article gives detailed information about the tests and analysis mentioned above.

The purpose of this paper is to increase the accuracy of the efficient portfolios frontier and the capital market line using the Riskiness Index.

This paper will develop the mean-riskiness model for portfolio selection using the Riskiness Index.

This paper’s main result is establishing a mean-riskiness efficient set of portfolios. In addition, the paper presents two applications for the mean-riskiness portfolio management method: one that is based on the multi-normal distribution (which is identical to the MV model optimal portfolio) and one that is based on the multi-normal inverse Gaussian distribution (which increases the portfolio’s accuracy, as it includes the a-symmetry and tail-heaviness features in addition to the scale and diversification features of the MV model).

The Riskiness Index is not a coherent measurement of financial risk, and the mean-riskiness model application is based on a high-order approximation to the portfolio’s rate of return distribution.

The mean-riskiness model increases portfolio management accuracy using the Riskiness Index. As the approximation order increases, the portfolio’s accuracy increases as well. This result can lead to a more efficient asset allocation in the capital markets.