Nowadays, short-term traffic flow forecasting has gained increasing attention from researchers due to traffic congestion in many large and medium-sized cities that pose a serious threat to sustainable urban development. To this end, this research examines the forecasting performance of functional time series modeling to forecast traffic flow in the ultra-short term. An appealing feature of the functional approach is that unlike other methods, it provides information over the whole day, and thus, forecasts can be obtained for any time within a day. Within this approach, a Functional AutoRegressive (FAR) model is used to forecast the next-day traffic flow. For empirical analysis, the traffic flow data of Dublin airport link road, Ireland, collected at a fifteen-minute interval from 1 January 2016 to 30 April 2017, are used. The first twelve months are used for model estimation, while the remaining four months are for the one-day-ahead out-of-sample forecast. For comparison purposes, a widely used model, namely AutoRegressive Integrated Moving Average (ARIMA), is also used to obtain the forecasts. Finally, the models’ performances are compared based on different accuracy statistics. The study results suggested that the functional time series model outperforms the traditional time series models. As the proposed method can produce traffic flow forecasts for the entire next day with satisfactory results, it can be used in decision making by transportation policymakers and city planners.

In the absence of a correct distribution theory for complex data, neutrosophic algebra can be very useful in quantifying uncertainty. In applied data analysis, implementation of existing gamma distribution becomes inadequate for some applications when dealing with an imprecise, uncertain, or vague dataset. Most existing works have explored distributional properties of the gamma distribution under the assumption that data do not have any kind of indeterminacy. Yet, analytical properties of the gamma model for the more realistic setting when data involved uncertainties remain largely underdeveloped. This paper fills such a gap and develops the notion of neutrosophic gamma distribution (NGD). The proposed distribution represents a generalized structure of the existing gamma distribution. The basic distributional properties, including moments, shape coefficients, and moment generating function (MGF), are established. Several examples are considered to emphasize the relevance of the proposed NGD for dealing with circumstances with inadequate or ambiguous knowledge about the distributional characteristics. The estimation framework for treating vague parameters of the NGD is developed. The Monte Carlo simulation is implemented to examine the performance of the proposed model. The proposed model is applied to a real dataset for the purpose of dealing with inaccurate and vague statistical data. Results show that the NGD has better flexibility in handling real data over the conventional gamma distribution.

Drought is one of the most common climatic or meteorological hazards and has spatiotemporal characteristics that substantially impact the livelihoods and economy worldwide. Therefore, there is a need for efficient procedures that accurately identify spatiotemporal variability. Moreover, it is crucial to continuously assess and monitor spatiotemporal drought occurrence in a certain region to prevent unfavourable impacts. For this purpose, the current study develops a new procedure for spatiotemporal analysis of the region: The Spatio-Temporal Weighted Joint Agglomerative Drought Index (STWJADI). The STWJADI is mainly based on a weighting scheme known as the Spatio-Temporal Two-Stage Standardized Weighting Scheme (STTSSWS). In the first stage of the STTSSWS, the steady-state probabilities are computed for several stations (Astor, Bunji, Chilas, Gupis, Skardu, and Gilgit) of the Northern region of Pakistan at a 1-month time scale (scale-1) to allocate weights for various drought classes. Moreover, in the second stage of the STTSSWS, the weights are allocated based on spatiotemporal weighting characteristics to acquire new weights for the numerous drought classes in the designated region. Further, the spatiotemporal weights attained from STTSSWS are utilized to compute the STWJADI. The outcomes of the STWJADI provide efficient and comprehensive information for drought characterization in the selected region.

This research aims to find the best model for predicting the Standardized Precipitation Index (SPI) and the Standardized Precipitation and Evapotranspiration Index (SPEI) in the future. The study estimates SPI and SPEI at different time scales, ranging from 1 to 48 months. To predict drought, Random Forest (RF) models are used based on lag times of 1–12 months for the estimated drought indices (SPI and SPEI). Accuracy and error metrics like Nash–Sutcliffe efficiency (NSE), root‐mean‐square error (RMSE), producer accuracy (PA), user accuracy (UA), and Choen’s kappa are used to assess the models. The NSE values for the SPI at varying time scales (1, 3, 6, 9, 12, and 48 months) indicate that Bahawalpur, Rawalpindi, Murree, and Sargodha stations have the highest NSE values of 0.1148, 0.5868, 0.8302, 0.9196, 0.9516, 0.9801, and 0.9845, respectively. Similarly, the RMSE values for SPI at these time scales show that Bahawalpur, Rawalpindi, Murree, and Sargodha stations have the lowest RMSE values of 0.6187, 0.6094, 0.4091, 0.2865, 0.2275, 0.1594, and 0.1106, respectively. The NSE and variance explained for SPI and SPEI at a 1‐month time scale were found to be poor, but they improved as the time scale increased. On the other hand, the RMSE values for SPI and SPEI at a 1‐month time scale were found to be high but decreased with longer time scales. The stations that exhibit the highest values of the NSE for the SPEI at various time scales (1, 3, 6, 9, 12, and 48 months) are Rawalpindi, Jhelum, Murree, Mianwali, Rawalpindi, and Sargodha, respectively. These stations have NSE values of 0.0784, 0.6074, 0.8353, 0.9225, 0.9542, 0.9760, and 0.9896, respectively. Similarly, the stations with the lowest RMSE values for SPEI at these time scales are Sargodha, Murree, Murree, Murree, Murree, and Sargodha, with RMSE values of 1.002, 0.5909, 0.3993, 0.2626, 0.2132, 0.1546, and 0.0941, respectively. The analysis reveals a distinct pattern indicating that stations situated at higher elevations exhibit a more pronounced correlation between the SPI and SPEI indices in comparison to stations at lower elevations. Notably, Murree, Jhelum, Sialkot, and Rawalpindi demonstrate a statistically significant and strong correlation between the SPI and SPEI. Overall, the results show that SPEI is a better drought index for classifying and monitoring meteorological drought in stations with lower elevations. However, in stations with higher elevations, the selected indices provide similar information, but with some differences.

The standardized precipitation index (SPI) is one of the most widely used indices for characterizing and monitoring drought in various regions. SPI's applicability has regional and time‐scale constraints when it observes in several homogeneous climatic regions with similar characteristics. It also does not provide sufficient knowledge about precipitation deficits and the spatiotemporal evolution of drought. Therefore, a new method, the regional spatially agglomerative continuous drought probability monitoring system (RSACDPMS), is proposed to obtain spatiotemporal information and monitor drought characteristics more expeditiously. The proposed framework uses spatially agglomerative precipitation (SAP) and copulas’ functions to continuously monitor the drought probability in the homogenous region. The RSACDPMS is validated in the region of the Northern area of Pakistan. The outcomes of the current study provide a better quantitative way to obtain appropriate information about precipitation deficits and the spatiotemporal evolution of drought.