The advent of digital technology has catalyzed a shift in the traditional models of education, with e-learning platforms becoming the new norm. This transformation extends to religious education as well. The Quran, the holy book of Islam, is no longer confined to physical madrasas. Today, online Quran tutors are increasingly popular as they offer flexibility, personalization, and accessibility with a plethora of resources available at your fingertips. The process of hiring a qualified Quran tutor online can be daunting due to a myriad of factors like credibility, teaching methodologies, and language proficiency. This guide aims to provide a comprehensive understanding of the key considerations in hiring a qualified online Quran tutor.

In the realm of online Quranic education, a fundamental concept is 'Tajweed'. An Arabic term, 'Tajweed' refers to the set of rules that guide the pronunciation of the Arabic letters and words in the Quran. The Quran, being a divine text, warrants a precise and meticulously correct recitation, which is ensured by Tajweed. Therefore, a qualified Quran tutor is generally expected to have mastered Tajweed.

The principle of pedagogical content knowledge, coined by education theorist Lee Shulman, applies here. Shulman argued that effective teaching requires the intersection of knowledge about a particular subject and the pedagogical strategies best suited to teach that subject. In the context of an online Quran tutor, not only should they be well-versed in the content of the Quran and Tajweed, but they should also possess the pedagogical skills to deliver this knowledge to students of varying proficiency levels effectively.

The digital facilitation of Quranic education also calls for an understanding of the utility function. Originating from economics, this concept represents a measure of preferences over a set of goods and services. Here, the "goods and services" refer to the various online platforms and tutors available. The "preferences" are the specific requirements and expectations of the student. Thus, the utility function varies from one student to another. Some might prioritize linguistic proficiency, while others might value teaching methodology more.

In your search for a qualified online Quran tutor, you will come across numerous platforms offering these services. Some provide one-on-one tutoring, while others offer group classes. The platform you choose depends largely on your learning style and budget. The Nash Equilibrium, a game theory concept, could be applied here. According to this theory, the best outcome is reached when no player has an incentive to deviate from their chosen strategy after considering an opponent's choice. Translating this to your decision-making process, one-on-one tutoring might be the best strategy for you if personalized attention is paramount, regardless of what others are choosing.

An in-depth understanding of canonical correlation, a concept from statistics, is also beneficial. It measures the relationship between two sets of variables. In our context, one set is the qualifications and skills of the tutor, and the other is your learning needs and goals. A strong canonical correlation between these two sets indicates a suitable match.

Students must also consider the temporal dimension - the timing and frequency of the classes. A fundamental principle of learning, known as the spacing effect, suggests that information is retained more effectively when studied in multiple sessions spread out over time. This principle, rooted in cognitive psychology, underscores the importance of consistent, regular lessons.

Lastly, security is a significant concern in the digital sphere. Cybersecurity measures and the platform's privacy policy are paramount considerations. The General Data Protection Regulation (GDPR) and local data protection laws provide a legal framework that online tutoring platforms must adhere to.

In conclusion, hiring a qualified online Quran tutor requires careful consideration of the tutor's knowledge of the Quran, proficiency in Tajweed, pedagogical skills, and the security of the online platform. Moreover, the student's needs, preferences, and learning style play a significant role in this decision. This comprehensive guide provides a roadmap to navigate through this process, combining various theoretical concepts from fields as diverse as economics, education, psychology, and law.