The family of 73-year-old Jerry Wayne Waller, the homeowner shot and killed by at least one Fort Worth police officer early Tuesday morning, issued a statement Wednesday afternoon.

In the statement, the family said the Fort Worth Police Department has been misrepresenting details of the incident to the media and they are calling for an independent investigation of what led to the fatal shooting.

Waller was shot and killed early Tuesday morning after he went outside to investigate bright lights outside of the bedroom, his wife Kathy told NBC 5 on Tuesday evening.

Armed with a .38-caliber pistol, Waller was apparently shot several times in his rear-facing garage after some sort of miscommunication with police officers.

Officials with the Fort Worth Police Department said officers were in the neighborhood responding to an alarm call; but that call was to a home across the street from the Waller residence.

Kathy said officers told her they thought the alarm call came from her residence.

The entire statement can be read below:

The immediate family of Jerry Wayne Waller of Fort Worth is shocked and deeply saddened by his untimely death in the privacy of his own home. Jerry was a dedicated family man and small business owner. As we mourn his loss, and celebrate his life, we ask that the media respect our privacy. Although we wish to devote this time with family and friends, we felt it was important to respond to the media coverage of this event. We were deeply troubled by the police department misrepresenting details of the incident in their interviews with the media. We would ask that the police refrain from providing details to the media until a thorough investigation has been completed, preferably by an independent body. On the night of his death, Jerry heard noise behind the house, and went to investigate. He picked up his gun as protection. While no one in the family was present at the instant of his death, his body was witnessed immediately after, inside his own garage. We were disturbed by suggestions that police may have felt threatened by a man in his own garage faced with unknown trespassers wielding flashlights. We look forward to a full investigation of this terrible incident that will lead to meaningful steps to ensure that nothing like this will happen again. Beyond the tragedy of his death, we hope that everyone will remember the spirit of Jerry’s life.

On Tuesday evening, Kathy spoke with NBC 5 and said she was "disgusted" by the shooting and said that the officers were "trigger happy."

"He would give you the shirt off his back, and he was loving, and he was a wonderful husband," Kathy Waller said Tuesday. "I think the police made a terrible mistake."

Another neighbor, former city council member Becky Haskin, said the alarm was triggered accidentally and that there never was a burglar in the area. Haskin said the fatal shooting was a "tragic accident."

Sgt. Kelly Peel, with the Fort Worth Police Department, said in a statement Wednesday afternoon, that the department is conducting a thorough and transparent investigation into the shooting and that once complete, it will be handed over to Chief Jeffrey Halstead for review.

Peel also revealed the names of the officers involved in the shooting, R.A. Hoeppner and B.B. Hanlon, who have been on the force since Oct., 2012.

Peel revealed no further details into the shooting or the investigation and said ti would be "inappropriate to comment any further ... until the investigation is complete."

Waller is survived by his wife, Kathy, to whom he was married for 46 years. Together they had three children and four grandchildren.

NBC 5's Randy McIlwain and Scott Gordon contributed to this report.