Log-logistic Research Articles

Scheduling of log logistics using a metaheuristic approach

An efficient log logistics plan results in log procurement cost savings. In practice, log logistics presents complexities such as synchronization of different machines, sorting of logs, and compatibility requirements. To address these complexities, this research proposes a decomposition approach for optimization of log logistics considering synchronization of log loaders and heterogeneous trucks at both cut blocks and sort yards. In the first phase, the daily number of truckloads between cut blocks and sort yards for each trucking contractor is determined, while allocation of the truckloads to compatible trucks and detailed routing and scheduling decisions are addressed in the second phase. Furthermore, a simulated annealing algorithm is developed for the second phase to obtain the schedules for large-sized problems. Additionally, the parameters of the algorithm are tuned using the Taguchi method. The algorithm is then applied to a case of a large Canadian forest company in British Columbia, Canada with a 1-month planning horizon. The results show that the proposed solution approach can successfully satisfy synchronization requirements and generate detailed schedules in a reasonable time. Also, cost savings for contractors are possible by assigning overtime rather than utilizing more trucks to fulfill their transportation tasks.

Marshall Olkin Exponentiated Dagum Distribution: Properties and Applications

Marshall Olkin Exponentiated Dagum distribution (MOED) with four shape parameters and one scale parameter is proposed. Alternative expressions are derived for the newly proposed distribution to sort out lengthy calculations. Various properties of MOED are derived, including the measure of central tendency, the measure of dispersion, hazard rate and survival rate are also derived for the MOED. Moreover, the network properties are also derived, including moments, moment generating function, quantile function, median, and mean deviation random number generator. Estimation of parameters is done through MLE (Maximum likelihood estimation) method, and to assess the value of the proposed distribution, the performance of the parameter’s estimates is studied through Monte Carlo Simulation. Three real-life data sets are used to evaluate the application and to scrutinize the performance of MOED as compared to the Marshall Olkin Dagum (MOD) distribution, Exponentiated Dagum (ED) distribution, Dagum (D) distribution, Burr III distribution, Kumaraswamy Burr III (KBurr III) distribution, Kumaraswamy Log Logistic (KLL) distribution and Log Logistic (LL) distribution. Four information criteria are used to examine the performance of the MOED with other special cases. The results showed that the newly proposed distribution performs better than the compared distributions.

Applications to Bio-Medical data and statistical inference for a Kavya-Manoharan log-logistic model

The log-logistic (LoL) distribution was studied by different authors, but in this article the Kavya-Manoharan log-logistic (KMLoL) distribution is proposed as a new extension of the LoL distribution. Furthermore, the new suggested distribution has two parameters, but it is a very flexible model, as evidenced by the application results. Some statistical features of the KMLoL distribution are derived. The parameters are estimated utilizing three techniques. A simulation study is carried out to evaluate the performance of three different estimation approaches. One real-world data set is utilized to highlight the importance and applicability of the proposed suggested model. The new suggested model compared to well-known distributions which have two, three and four parameters, also it outperform them all of these models.

Attribute control chart based on SkSP-R scheme under assumption of Log-logistic (LL) distribution

Attribute control chart based on SkSP-R scheme under assumption of Log-logistic (LL) distribution

A Formulation of the Log-Logistic Distribution for Fading Channel Modeling

In some scenarios, the log-logistic (LL) distribution is shown to provide the best fit to field measurements in the context of wireless channel modeling. However, a fading channel model based on the LL distribution has not been formulated yet. In this work, we introduce the L-distribution as a reformulation of the LL distribution for channel modeling purposes. We provide closed-form expressions for its PDF, CDF, and moments. Performance analysis of wireless communication systems operating under L-fading channels is exemplified, providing exact and asymptotic expressions for relevant metrics such as the outage probability and the average capacity. Finally, important practical aspects related to the use of the L-distribution for channel fitting purposes are discussed in two contexts: (i) millimeter-wave links with misaligned gain, and (ii) air–ground channels in unmanned aerial vehicle communications.

Social-Demographic and Cultural Determinants of Nigerian Women's Age at First Birth Using the Log Logistics Accelerated Failure Time Model

Early age at first birth has many negative effects on women which includes but are not limited to truncation in education, maternal mortality, sexually transmitted infections, difficulties resulting from pregnancy before a woman is physically mature, cervical cancer, and missing life opportunities in general. In this study, we determined the factors that influence the age at first birth so as to promote child and maternal health in Nigeria. Secondary data from the 2018 Nigeria Demographic and Health Surveys (NDHS) and the Accelerated Failure Time (AFT) model were used in this study to establish the determinants of a woman’s age at first birth in Nigeria. The Log logistics AFT model was used after the dataset failed to satisfy the Cox Proportional Hazard (CPH) model’s assumption. The results show that women from the North Central (NC) will give birth before the women in the North West (NW) and South South (SS). Those with no education will give birth earlier than those with secondary education. Women who do not know their husband’s status will give birth earlier than those that want the same thing as their husband. The women that are more exposed to early first birth as discovered from this study should be empowered and educated so as to discourage early marriage. Policy makers should take decisions to help promote the health of the mother and her child. This will reduce the number of school dropout of women and more opportunities for women over the course of life.

A goal programming model for the optimization of log logistics considering sorting decisions and social objective

Log logistics include sorting, processing, and transporting of logs from their place of harvest to demand locations. These activities account for a significant portion of the total log procurement costs; therefore, attempts were made in previous studies to optimize some aspects of log logistics. However, operational details, such as sorting decisions, truck compatibility requirements, and social objectives, are often disregarded in the optimization literature. Incorporating these details into the model makes the results more realistic and applicable. To address these gaps, a bi-objective mixed-integer programming model is developed in this paper to optimize log logistics. The first objective is to minimize total logistics costs, and the second objective is to provide a balanced workload for trucking contractors. The bi-objective model is solved using the goal programming approach. The model is applied to log logistics of a large Canadian forest company, where trucking contractors use heterogeneous fleet of trucks to carry various log sorts from cutblocks to sort yards for sorting. The planning horizon is 4 weeks with daily decisions. The goal programming model generates balanced workloads for the contractors with less than 0.4% increase in total costs compared to the single objective model where only the total cost is minimized.

Marshall–Olkin Extended Gumbel Type‐II Distribution: Properties and Applications

Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall–Olkin Extended Gumbel Type‐II (MOEGT‐II) which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J‐shaped, and upside down bathtub shapes of the failure rate function. Various statistical properties of the proposed distribution are derived such as alternate expressions for the density and distribution function, special cases of MOEGT‐II distribution, quantile function, Lorenz curve, and Bonferroni curve. Estimation of the unknown parameters is carried out by the method of maximum likelihood. A simulation study is conducted using three different iterative methods with different samples of sizes n. The usefulness and potentiality of the MOEGT‐II distribution have been shown using three real life data sets. The MOEGT‐II distribution has been demonstrated as better fit than Exponentiated Gumbel Type‐II (EGT‐II), Marshall–Olkin Gumbel Type‐II (MOGT‐II), Gumbel Type‐II (GT‐II), Marshall–Olkin–Frechet (MOF), Frechet (F), Burr III, Log Logistic (LL), Beta Inverse Weibull (BIW), and Kumaraswamy Inverse Weibull (KIW) distributions.

Estimation of Entropy for Log‐Logistic Distribution under Progressive Type II Censoring

Entropy is a useful indicator of information content that has been used in a number of applications. The Log‐Logistic (LL) distribution is a probability distribution that is often employed in survival analysis. This paper addresses the problem of estimating multiple entropy metrics for an LL distribution using progressive type II censoring. We derive formulas for six different types of entropy measurements. To obtain the estimators of the proposed entropy measures, the maximum likelihood approach is applied. Approximate confidence intervals are calculated for the entropy metrics under discussion. A numerical evaluation is performed using various censoring methods and sample sizes to characterize the behavior of estimator’s measures using relative biases, related mean squared errors, average interval lengths, and coverage probabilities. Numerical analysis revealed that the accuracy measures improve with sample size, and the suggested entropy estimates approach the genuine values as censoring levels decrease. Finally, an actual dataset was evaluated for demonstration purposes.

Multivariate and multi-temporal analysis of meteorological drought in the northeast of Thailand

This study evaluates drought characteristics in the Mun River Basin, located in the northeast of Thailand. The basin is important from an agriculture perspective, as about 75% of the total area is under cultivation (a majority of which is without irrigation facilities). It is, however, also one of the most drought-prone regions in the country, and a proper understanding of drought characteristics can aid in planning and implementing drought mitigation and management strategies and measures in the basin. Using the Standardized Precipitation Evapotranspiration Index (SPEI), calculated from high-resolution climatic data during 1979–2017, we find that major drought events recur approximately every 6 years in the basin. A new approach to the use of thresholds to remove the effects of minor droughts is introduced. It is found to have improved drought characterization for prolonged drought events with low intensity. Drought events are evaluated for severity, duration, and frequency (SDF) using univariate and multivariate approaches at nine timescales (1-week to 24-months). Generalized Extreme Value (GEV) and Log-logistic (LL) are the most suitable distributions for SPEI calculation in the study area, though all three-parameter distributions have good fit at longer timescales. SPEI calculated at weekly timescales, especially during the vegetative stage of crop growth, show a good correlation with yields; thus, they can be useful for planning agricultural activities. Drought vulnerable assessment using joint occurrence probabilities of drought duration and severity indicates that most of the area in the western part and some area in the eastern part are the highest drought-prone regions in the basin. It is interesting to note that the drought prone areas of the basin are independent of the annual rainfall amount but are influenced by its temporal variability.

An Assessment of Incorporating Log-Logistic Testing Effort Into Imperfect Debugging Delayed S-Shaped Software Reliability Growth Model

Software reliability growth models (SRGM) are employed to aid us in predicting and estimating reliability in the software development process. Many SRGM proposed in the past claim to be effective over previous models. While some earlier research had raised concern regarding use of delayed S-shaped SRGM, researchers later indicated that the model performs well when appropriate testing-effort function (TEF) is used. This paper proposes and evaluates an approach to incorporate the log-logistic (LL) testing-effort function into delayed S-shaped SRGMs with imperfect debugging based on non-homogeneous Poisson process (NHPP). The model parameters are estimated by weighted least square estimation (WLSE) and maximum likelihood estimation (MLE) methods. The experimental results obtained after applying the model on real data sets and statistical methods for analysis are presented. The results obtained suggest that performance of the proposed model is better than the other existing models. The authors can conclude that the log-logistic TEF is appropriate for incorporating into delayed S-shaped software reliability growth models.

Evaluation of Parametric Method Performance for Left-Censored Data and Recommendation of Using for Covid-19 Data Analysis

bjectives: Left-censored data, which is commonly seen in clinical studies, are frequently encountered in the literature, especially in the fields of food, environment, microbiology, and biochemistry. In this study, the most appropriate distribution between the negatively skewed distributions for left-censored data in Parametric Inverse Hazard Models was tried to be determined. Methods: Within the scope of the study, firstly, the data were produced uncensored according to different parameters of each distribution. Then, simulation studies were carried out in different censorship rates (15%, 25% and 35%) and various sample sizes (1000, 2000 and 3000) in order to determine the most appropriate distribution. AIC, AICC, HQIC, and CAIC information criteria were employed to compare the distribution performances. Since it was not possible to study simulations of all possible scenarios, scenarios similar to each other were generally preferred over others. Results: In the simulation results, the most appropriate distributions to be used for left-censored data in Parametric Inverse Hazard Models were found as Generalized Inverse Weibull as well as Log-Logistic, Log-Normal, Inverse Normal and Gamma distributions. It was also detected that the Marshal-Olkin distribution revealed a superior performance compared to the Modified Weibull, Generalized Gamma, Gamma, and Flexible Weibull distributions. Log logistics distribution gave the most appropriate result among the analyzed distributions in the examination made with real data application. Conclusion: The use of censored data analysis in evaluations in terms of Covid-19 is quite additive, considering that more statistical evaluation will be needed in the next period of the epidemic. Improved estimates can be obtained with this approach, especially in Covid-19 data analysis. Keywords: Covid-19, left-censored, limit of detection, Parametric Inverse Hazard Models

A comparison between the performance of Weibull and Log-logistic Aging Models on Saccharomyces cerevisiae lifespan data

Empirical lifespan datasets are often studied with the best-fitted mathematical model for aging. In this study, we focus our attention to the budding yeast S. cerevisiae lifespan and the determination of the best-fitted model of aging. We investigate the influence of model selection in yeast lifespan datasets and the fitting outcomes of the two-parameter Weibull (WE) and Log-logistic (LL) models of aging. Both of these models are commonly studied and implemented in aging research. They show similar tendency as a survival function that they correspond to mortality rates that increase, and then decrease, with time. Studies so far has been usually done with medflies, Drosophila, house flies, flour beetles, and humans with these models. Different than previous research, we focus our attention on the influence of fitting results and calibrations on empirical lifespan data samples. As expected both of the models could be used as a substitute of each other. However, we also find WE model fits the yeast lifespan data significantly better than LL model with an R 2 = 0.86. This finding is especially important in yeast aging study because of typically survival models are applied and therefore one can see which model fits the yeast data best. In this article, comparisons are done and developed and the potential of the approach is demonstrated with a model comparison of yeast replicative lifespan datasets of the laboratory BY4741 and BY4742 wildtype reference strains. Our study highlights that interpreting model fitting results of experimental lifespans should take model selection and resulted variation into account.

Is there a universal parametric city size distribution? Empirical evidence for 70 countries

We studied the parametric description of the city size distribution (CSD) of 70 different countries (developed and developing) using seven models, as follows: the lognormal (LN), the loglogistic (LL), the double Pareto lognormal (dPLN), the two-lognormal (2LN), the two-loglogistic (2LL), the three-lognormal (3LN) and the three-loglogistic (3LL). Our results show that 3LN and 3LL are the best densities in terms of non-rejections out of standard statistical tests. Meanwhile, according to the information criteria AIC and BIC, there is no systematically dominant distribution.

Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data

In this paper, a new three-parameter lifetime distribution is introduced; the new model is a generalization of the log-logistic (LL) model, and it is called the alpha power transformed log-logistic (APTLL) distribution. The APTLL distribution is more flexible than some generalizations of log-logistic distribution. We derived some mathematical properties including moments, moment-generating function, quantile function, Rényi entropy, and order statistics of the new model. The model parameters are estimated using maximum likelihood method of estimation. The simulation study is performed to investigate the effectiveness of the estimates. Finally, we used one real-life dataset to show the flexibility of the APTLL distribution.

Comparative analysis of probability distributions for the Standardized Precipitation Index and drought evolution in China during 1961–2015

As a representative index for monitoring and assessing drought, the Standardized Precipitation Index (SPI) relies on a suitable probability distribution function (PDF) to describe a precipitation series, which allows interregional comparisons following normalization. In this study, we considered nine PDFs (exponential (EXP), extreme value (EV), gamma (GAM), generalized Pareto (GP), logistic (LO), log-logistic (LOL), log-normal (LON), normal (NOR), and Weibull (WEI)) as candidates for use in SPI calculations. Based on monthly precipitation time series data (1961–2015) from 582 stations across China, together with the Kolmogorov–Smirnov (K–S) and Akaike Information Criterion (AIC) methods, differences in optimal PDFs for SPI calculations were compared comprehensively from the perspectives of timescale, record length, and index value. Based on the SPI calculated using the optimal PDF at the 6-month timescale (SPI6-opt), we analyzed the spatiotemporal characteristics of drought trends in China using the Mann–Kendall method. Results indicated both the timescale and the record length would affect the selection of the optimal PDF. The performance of the WEI and GAM distributions was superior to other distributions in describing monthly precipitation (especially for long precipitation records) at short and multiple timescales, respectively. During the entire study period, areas of China with high frequency of drought have transferred from the northwest (1960s), to the northeast (2000s), and to the southwest (most recent 5 years). Trend analysis revealed a noticeable wetting tendency confined mainly to Northwest, Northeast, and Southeast China and a significant trend toward drought in Southwest China and on the North China Plain.

Entwicklung und Evaluation eines Wiegesystems für Forstkräne auf Basis von künstlichen neuronalen Netzen

Sowohl in der Hackschnitzel- als auch Rundholzlogistik fehlen oft wichtige Referenzmengen fur den dispositiven Einsatz, welche zumeist mit unzureichend genauen Schatzwerten vervollstandigt werden. Um die Informationsqualitat uber die bewegten Holzmengen zu verbessern, konnen optional Kranwaagen zwischen Teleskopauge und Greifer am Kran des Forwarders montiert werden. Dies beeinflusst jedoch die Krankinematik und Manovrierfahigkeit negativ, bei zeitgleich sinkender Maschinenproduktivitat aufgrund einer zur Messung notwendigen Unterbrechung des Ladeprozesses. In diesem Beitrag wird eine datenbasierte Methode prasentiert, welche einen dynamischen Wiegeprozess im kontinuierlichen Ladevorgang bei modernen Forstkranen ermoglicht, ohne dass eine zusatzliche Hardware-Komponente auf der Maschine verbaut werden muss. Bei dieser Methode wird ein Ladezyklus automatisiert erkannt und die geladene Masse anhand eines kunstlichen neuronalen Netzwerkes (KNN) abgeschatzt. Als Eingangsgrosen dienen Signale von Sensoren, die auf auf modernen Forwardern serienmasig installiert sind. Fur die Verarbeitung von zeitbasierten Sensordaten in einem neuronalen Netz hat sich die Long-Short-Term-Memory(LSTM)-Architektur bewahrt. Basierend auf LSTM-Zellen wurde ein entsprechendes Netzwerk entworfen, trainiert und anschliesend optimiert. Im Test zeigt sich fur einen einzelnen Ladezyklus ein mittlerer Gesamtskalenfehler von 1,5 %, bezogen auf 1.000 kg. Fur einen voll beladenen Forwarder resultiert dies in einem Gesamtmassenfehler kleiner 1,2 %.

Survival Modeling on Non Active Students’ Study of Universitas Terbuka: A Case Study

Survival analysis is a statistical method, a part of the Generalized Linear Models, used to study the survival time of an individual to an event. The application of survival analysis is indispensable in open and distance education, like Universitas Terbuka (UT), Indonesia. This analysis can determine students’ durability of study opportunities within a certain time. The analysis showed that the appropriate survival model to describe the covariate that was supposed to influence the study durability of the UT students of the Non Basic Education Program was Log Logistics. Covariate that influenced the survival of study was course of study, age, marital status, employment status, educational background, number of credits taken, 1st semester’s result, Grade Point Average (GPA), and the courses taken per semester.

Characteristics and Application of the NHPP Log-Logistic Reliability Model

In this paper, a Nonhomogeneous Poisson Process (NHPP) reliability model based on the two-parameter Log-Logistic (LL) distribution is considered. The essential model’s characteristics are derived and represented graphically. The parameters of the model are estimated by the Maximum Likelihood (ML) and Non-linear Least Square (NLS) estimation methods for the case of time domain data. An application to show the flexibility of the considered model are conducted based on five real data sets and using three evaluation criteria. We hope this model will help as an alternative model to other useful reliability models for describing real data in reliability engineering area.

Assessing Survival Time of Women with Cervical Cancer Using Various Parametric Frailty Models: A Case Study at Tikur Anbessa Specialized Hospital, Addis Ababa, Ethiopia

Cervical cancer is one of the leading causes of death in the world and represents a tremendous burden on patients, families and societies. It is estimated that over one million women worldwide currently have cervical cancer; most of them have not been diagnosed or have no access to treatment that could cure them or prolong their lives. The goal of this study is to investigate potential risk factors affecting survival time of women with cervical cancer at Tikur Anbessa specialized hospital. Data were taken from patients’ medical record card that enrolled during September 2011–September 2015. Kaplan–Meier estimation method, Cox proportional hazard model and parametric shared frailty model were used to analysis survival time of cervical cancer patients. Study subjects (cervical cancer patients) in this study came from clustered community and hence clustered survival data correlated at the regional level. Parametric frailty models will be explored assuming that women with in the same cluster (region for this study) shares similar risk factors. We used Exponential, Weibull, Log logistics and Log normal distributions and based on AIC criteria, all models were compared for their performance. The lognormal inverse Gaussian model has the minimum AIC value among the models compared. The results implied that not giving birth up to the study ends and married after twenty years were significantly prolong the survival time of patients while age class 51–60, 61–70, > 70, smoking cigarettes, patients with stage III and IV disease, family history of cervical cancer, history of abortion and living with HIV AIDS were significantly shorten survival time of patients. The findings of this study suggested that age, smoking cigarettes, stage, family history, abortion history, living with HIV AIDS, age at first marriage and age at first birth were major factors to survival time of patients. Heterogeneity between the regions in the survival time of cervical cancer patients, indicating that one needs to account for this clustering variable using frailty models. The fit statistics showed that lognormal inverse-Gaussian frailty model described the survival time of cervical cancer patients dataset better than other distributions used in this study.