“Inside Out 2,” starring a personified Anxiety, continued to resonate with moviegoers as the No. 1 film in North America for a third weekend. The dread-infused prequel “A Quiet Place: Day One” also struck a cultural nerve, arriving to stronger-than-expected ticket sales.

But ticket buyers largely rebuffed Kevin Costner’s three-hour vanity project, “Horizon: An American Saga — Chapter 1,” the supposed start of an Old West movie series that was once headed straight to a streaming service before managing to get bumped up to the big screen.

“Inside Out 2” from Pixar was on pace to collect $55 million, for a three-week total of roughly $470 million in the United States and Canada, according to estimates by box office analysts on Saturday. The well-reviewed sequel is nearing $1 billion in worldwide ticket sales. No movie has reached that sales threshold since “Barbie,” which was released in July 2023.

For the weekend, “A Quiet Place: Day One” was expected to generate about $53 million in domestic ticket sales — more than 30 percent above prerelease analyst expectations, which are based on surveys that track moviegoer interest. “A Quiet Place: Day One,” which cost Paramount an estimated $67 million to make, stars Lupita Nyong’o as a cancer patient who, with her cat, Frodo, must navigate a horrific invasion by alien creatures with extra-sensitive ears.

Prequels are risky. Prominent misfires have included “Furiosa: A Mad Max Saga,” “The First Omen” and “Lightyear.” Fans already know what ultimately happens later in the story, making it hard for studio marketers to generate excitement, and prequels often lack the stars who helped make the franchises popular in the first place. Emily Blunt, for instance, headlined the first two “Quiet Place” movies.

The strong showing for “Day One” is even more impressive given that its studio, Paramount, has recently been caught in a distracting sale drama. The company’s controlling shareholder, Shari Redstone, ousted a top executive, haggled over a takeover offer and, finally, called the whole thing off, sending the stock price tumbling. Despite that upheaval, Paramount’s movie team expertly eased “Day One” into the marketplace.

Mr. Costner’s heavily publicized “Horizon,” which cost an estimated $100 million to make and another $30 million to market, arrived as a distant third. It was on pace to earn $12 million, analysts said. (Theaters and studios split ticket sales roughly 50-50.) Mr. Costner had been holding out hope that fans of the hit contemporary Western series “Yellowstone,” particularly those in the middle of the country, would flock to theaters. It proved to be a pipe dream.

Could “Horizon” gain its footing in the coming weeks? Box office experts were not optimistic, citing weak reviews. In addition, ticket buyers gave “Horizon” a grade of B-minus in CinemaScore exit polls, which means that word of mouth will be soft.

Warner Bros. will release the second chapter on Aug. 16. Mr. Costner has already started to make Part 3 and has also announced a fourth installment.

Warner Bros. is only serving as a distributor for hire, meaning that the studio has invested nothing in the films and, therefore, has no financial exposure. (The company will receive a cut of ticket sales — about 8 percent — as a fee for its services.) To finance the project, Mr. Costner mortgaged real estate in Santa Barbara, Calif., and lined up support from private investors. He left “Yellowstone” to focus on “Horizon.”

“There are movies that overcome the odds, break the mold and prove the skeptics wrong,” said David A. Gross, a film consultant who publishes a newsletter on box office numbers. “In this case, the mold is still intact: Westerns are not in fashion, and there hasn’t been a successful theatrical Western series in the last 50 years.”